仕事の部屋

2016年7月17日日曜日

160717(3)

整数列のLINKS の編集(56)

https://oeis.org/A205988

https://oeis.org/A186742
のLINKS を編集しました。

160717(2)

整数列のLINKS の編集(55)

https://oeis.org/A274472
のLINKS を編集しました。

160717

整数列のLINKS の編集(54)

https://oeis.org/A001522
のLINKS を編集しました。

2016年7月12日火曜日

160712

Ruby

平面的2進数(2)

1 を足していってn にするのではなく、直接n を求めてみた。

def f(n)
  # lは大きめ
  l = 100
  a = Array.new(l){Array.new(l, 0)}
  a[0][0] = n
  flag = true
  m, x = 0, 0
  while flag
    flag = false
    (0..m).each{|i|
      a[i][m - i], j = a[i][m - i] % 2, a[i][m - i] / 2
      if j > 0
        flag = true
        x = [i + 1, x].max
        a[i + 1][m - i] += j
        a[i][m - i + 1] += j
      end
    }
    m += 1
  end
  (0..x).each{|i| p a[x - i][0..x].reverse}
  return ""
end

(0..37).each{|i|
  p i
  p f(i)
}

出力結果
0
[0]
""
1
[1]
""
2
[0, 1]
[1, 0]
""
3
[0, 1]
[1, 1]
""
4
[0, 1, 1]
[1, 0, 0]
[1, 0, 0]
""
5
[0, 1, 1]
[1, 0, 0]
[1, 0, 1]
""
6
[0, 1, 1]
[1, 0, 1]
[1, 1, 0]
""
7
[0, 1, 1]
[1, 0, 1]
[1, 1, 1]
""
8
[0, 1, 1, 1]
[1, 0, 1, 0]
[1, 1, 0, 0]
[1, 0, 0, 0]
""
9
[0, 1, 1, 1]
[1, 0, 1, 0]
[1, 1, 0, 0]
[1, 0, 0, 1]
""
10
[0, 1, 1, 1]
[1, 0, 1, 0]
[1, 1, 0, 1]
[1, 0, 1, 0]
""
11
[0, 1, 1, 1]
[1, 0, 1, 0]
[1, 1, 0, 1]
[1, 0, 1, 1]
""
12
[0, 1, 1, 1, 0]
[1, 0, 1, 0, 1]
[1, 1, 0, 0, 1]
[1, 0, 0, 0, 0]
[0, 1, 1, 0, 0]
""
13
[0, 1, 1, 1, 0]
[1, 0, 1, 0, 1]
[1, 1, 0, 0, 1]
[1, 0, 0, 0, 0]
[0, 1, 1, 0, 1]
""
14
[0, 1, 1, 1, 0]
[1, 0, 1, 0, 1]
[1, 1, 0, 0, 1]
[1, 0, 0, 0, 1]
[0, 1, 1, 1, 0]
""
15
[0, 1, 1, 1, 0]
[1, 0, 1, 0, 1]
[1, 1, 0, 0, 1]
[1, 0, 0, 0, 1]
[0, 1, 1, 1, 1]
""
16
[0, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 0]
[1, 1, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
""
17
[0, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 0]
[1, 1, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 1]
""
18
[0, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 0]
[1, 1, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 1]
[0, 1, 0, 0, 1, 0]
""
19
[0, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 0]
[1, 1, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 1]
[0, 1, 0, 0, 1, 1]
""
20
[0, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 0]
[1, 1, 1, 0, 1, 1]
[1, 0, 0, 1, 0, 0]
[0, 1, 0, 1, 0, 0]
""
21
[0, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 0]
[1, 1, 1, 0, 1, 1]
[1, 0, 0, 1, 0, 0]
[0, 1, 0, 1, 0, 1]
""
22
[0, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 0]
[1, 1, 1, 0, 1, 1]
[1, 0, 0, 1, 0, 1]
[0, 1, 0, 1, 1, 0]
""
23
[0, 1, 1, 1, 1, 0]
[1, 0, 1, 1, 0, 1]
[1, 1, 0, 1, 0, 0]
[1, 1, 1, 0, 1, 1]
[1, 0, 0, 1, 0, 1]
[0, 1, 0, 1, 1, 1]
""
24
[0, 1, 1, 1, 1, 0, 0]
[1, 0, 1, 1, 0, 1, 0]
[1, 1, 0, 1, 0, 0, 1]
[1, 1, 1, 0, 0, 1, 1]
[1, 0, 0, 0, 0, 1, 0]
[0, 1, 0, 1, 1, 0, 0]
[0, 0, 1, 1, 0, 0, 0]
""
25
[0, 1, 1, 1, 1, 0, 0]
[1, 0, 1, 1, 0, 1, 0]
[1, 1, 0, 1, 0, 0, 1]
[1, 1, 1, 0, 0, 1, 1]
[1, 0, 0, 0, 0, 1, 0]
[0, 1, 0, 1, 1, 0, 0]
[0, 0, 1, 1, 0, 0, 1]
""
26
[0, 1, 1, 1, 1, 0, 0]
[1, 0, 1, 1, 0, 1, 0]
[1, 1, 0, 1, 0, 0, 1]
[1, 1, 1, 0, 0, 1, 1]
[1, 0, 0, 0, 0, 1, 0]
[0, 1, 0, 1, 1, 0, 1]
[0, 0, 1, 1, 0, 1, 0]
""
27
[0, 1, 1, 1, 1, 0, 0]
[1, 0, 1, 1, 0, 1, 0]
[1, 1, 0, 1, 0, 0, 1]
[1, 1, 1, 0, 0, 1, 1]
[1, 0, 0, 0, 0, 1, 0]
[0, 1, 0, 1, 1, 0, 1]
[0, 0, 1, 1, 0, 1, 1]
""
28
[0, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 0, 1, 1, 1]
[1, 0, 0, 0, 0, 0, 0, 1]
[0, 1, 0, 1, 0, 0, 0, 1]
[0, 0, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 1, 1, 1, 0, 0]
""
29
[0, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 0, 1, 1, 1]
[1, 0, 0, 0, 0, 0, 0, 1]
[0, 1, 0, 1, 0, 0, 0, 1]
[0, 0, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 1, 1, 1, 0, 1]
""
30
[0, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 0, 1, 1, 1]
[1, 0, 0, 0, 0, 0, 0, 1]
[0, 1, 0, 1, 0, 0, 0, 1]
[0, 0, 1, 1, 0, 0, 0, 1]
[0, 0, 0, 1, 1, 1, 1, 0]
""
31
[0, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 0, 1, 1, 1]
[1, 0, 0, 0, 0, 0, 0, 1]
[0, 1, 0, 1, 0, 0, 0, 1]
[0, 0, 1, 1, 0, 0, 0, 1]
[0, 0, 0, 1, 1, 1, 1, 1]
""
32
[0, 1, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 1, 0, 0, 0, 1]
[1, 1, 1, 1, 0, 0, 1, 1, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 1, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0, 0]
""
33
[0, 1, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 1, 0, 0, 0, 1]
[1, 1, 1, 1, 0, 0, 1, 1, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 1, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0, 1]
""
34
[0, 1, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 1, 0, 0, 0, 1]
[1, 1, 1, 1, 0, 0, 1, 1, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 1, 0, 0, 0, 1]
[0, 0, 0, 1, 0, 0, 0, 1, 0]
""
35
[0, 1, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 1, 0, 0, 0, 1]
[1, 1, 1, 1, 0, 0, 1, 1, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 1, 0, 0, 0, 1]
[0, 0, 0, 1, 0, 0, 0, 1, 1]
""
36
[0, 1, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 1, 0, 0, 0, 1]
[1, 1, 1, 1, 0, 0, 1, 1, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 1, 0, 0, 1, 1]
[0, 0, 1, 0, 1, 0, 1, 0, 0]
[0, 0, 0, 1, 0, 0, 1, 0, 0]
""
37
[0, 1, 1, 1, 1, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 1, 0, 0, 1, 0]
[1, 1, 1, 0, 1, 0, 0, 0, 1]
[1, 1, 1, 1, 0, 0, 1, 1, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 1, 0, 0, 1, 1]
[0, 0, 1, 0, 1, 0, 1, 0, 0]
[0, 0, 0, 1, 0, 0, 1, 0, 1]
""

2016年7月10日日曜日

160710

Ruby

平面的2進数(1)

せきゅーんさんの記事（http://integers.hatenablog.com/entry/2016/07/05/232148）を見て、
butchi氏が卒業論文（http://butchi.jp/documents/b-thesis.pdf）で研究したという

平面的2進数を計算しようと思った。

n = 37
# Nは大きめ
N = 50
a = Array.new(N){Array.new(N, 0)}
p 0
p [0]
p ""
max = 0
n.times{|i|
  a[0][0] += 1
  (0..N - 1).each{|i|
    (0..N - 1).each{|j|
      if a[i][j] > 1
        a[i][j] %= 2
        a[i + 1][j] += 1
        a[i][j + 1] += 1
        max = [max, j + 1].max
      end
    }
  }
  p i + 1
  (0..max).each{|i| p a[max - i][0..max].reverse}
  p ""
}

2016年7月9日土曜日

160709(2)

Ruby

Numbers n such that 2 * n^2 - 1 is a square(3)

コードをシンプルにした。

n = 100
x, y = 1, 0
(n + 1).times{|i|
  x = 2 * y + x
  y = 2 * x + y
  a, b, c = (y - x - 1) / 2, (y - x + 1) / 2, x
  p [i, [a, b, c], a * a + b * b == c * c]
}

出力結果
[0, [0, 1, 1], true]
[1, [3, 4, 5], true]
[2, [20, 21, 29], true]
[3, [119, 120, 169], true]
[4, [696, 697, 985], true]
[5, [4059, 4060, 5741], true]
[6, [23660, 23661, 33461], true]
[7, [137903, 137904, 195025], true]
[8, [803760, 803761, 1136689], true]
[9, [4684659, 4684660, 6625109], true]
[10, [27304196, 27304197, 38613965], true]
[11, [159140519, 159140520, 225058681], true]
[12, [927538920, 927538921, 1311738121], true]
[13, [5406093003, 5406093004, 7645370045], true]
[14, [31509019100, 31509019101, 44560482149], true]
[15, [183648021599, 183648021600, 259717522849], true]
[16, [1070379110496, 1070379110497, 1513744654945], true]
[17, [6238626641379, 6238626641380, 8822750406821], true]
[18, [36361380737780, 36361380737781, 51422757785981], true]
[19, [211929657785303, 211929657785304, 299713796309065], true]
[20, [1235216565974040, 1235216565974041, 1746860020068409], true]
[21, [7199369738058939, 7199369738058940, 10181446324101389], true]
[22, [41961001862379596, 41961001862379597, 59341817924539925], true]
[23, [244566641436218639, 244566641436218640, 345869461223138161], true]
[24, [1425438846754932240, 1425438846754932241, 2015874949414289041], true]
[25, [8308066439093374803, 8308066439093374804, 11749380235262596085], true]
[26, [48422959787805316580, 48422959787805316581, 68480406462161287469], true]
[27, [282229692287738524679, 282229692287738524680, 399133058537705128729], true]
[28, [1644955193938625831496, 1644955193938625831497, 2326317944764069484905], true]
[29, [9587501471344016464299, 9587501471344016464300, 13558774610046711780701], true]
[30, [55880053634125472954300, 55880053634125472954301, 79026329715516201199301], true]
[31, [325692820333408821261503, 325692820333408821261504, 460599203683050495415105], true]
[32, [1898276868366327454614720, 1898276868366327454614721, 2684568892382786771291329], true]
[33, [11063968389864555906426819, 11063968389864555906426820, 15646814150613670132332869], true]
[34, [64485533470821007983946196, 64485533470821007983946197, 91196316011299234022705885], true]
[35, [375849232435061491997250359, 375849232435061491997250360, 531531081917181734003902441], true]
[36, [2190609861139547943999555960, 2190609861139547943999555961, 3097990175491791170000708761], true]
[37, [12767809934402226172000085403, 12767809934402226172000085404, 18056409971033565286000350125], true]
[38, [74416249745273809088000956460, 74416249745273809088000956461, 105240469650709600546001391989], true]
[39, [433729688537240628356005653359, 433729688537240628356005653360, 613386407933224037990008001809], true]
[40, [2527961881478169961048032963696, 2527961881478169961048032963697, 3575077977948634627394046618865], true]
[41, [14734041600331779137932192128819, 14734041600331779137932192128820, 20837081459758583726374271711381], true]
[42, [85876287720512504866545119809220, 85876287720512504866545119809221, 121447410780602867730851583649421], true]
[43, [500523684722743250061338526726503, 500523684722743250061338526726504, 707847383223858622658735230185145], true]
[44, [2917265820615946995501486040549800, 2917265820615946995501486040549801, 4125636888562548868221559797461449], true]
[45, [17003071238972938722947577716572299, 17003071238972938722947577716572300, 24045973948151434586670623554583549], true]
[46, [99101161613221685342183980258883996, 99101161613221685342183980258883997, 140150206800346058651802181530039845], true]
[47, [577603898440357173330156303836731679, 577603898440357173330156303836731680, 816855266853924917324142465625655521], true]
[48, [3366522229028921354638753842761506080, 3366522229028921354638753842761506081, 4760981394323203445293052612223893281], true]
[49, [19621529475733170954502366752732304803, 19621529475733170954502366752732304804, 27749033099085295754434173207717704165], true]
[50, [114362654625370104372375446673632322740, 114362654625370104372375446673632322741, 161733217200188571081311986634082331709], true]
[51, [666554398276487455279750313289061631639, 666554398276487455279750313289061631640, 942650270102046130733437746596776286089], true]
[52, [3884963735033554627306126433060737467096, 3884963735033554627306126433060737467097, 5494168403412088213319314492946575384825], true]
[53, [22643228011924840308557008285075363170939, 22643228011924840308557008285075363170940, 32022360150370483149182449211082676022861], true]
[54, [131974404336515487224035923277391441558540, 131974404336515487224035923277391441558541, 186639992498810810681775380773549480752341], true]
[55, [769203198007168083035658531379273286180303, 769203198007168083035658531379273286180304, 1087817594842494380941469835430214208491185], true]
[56, [4483244783706493010989915264998248275523280, 4483244783706493010989915264998248275523281, 6340265576556155474967043631807735770194769], true]
[57, [26130265504231789982903833058610216366959379, 26130265504231789982903833058610216366959380, 36953775864494438468860791955416200412677429], true]
[58, [152298348241684246886433083086663049926232996, 152298348241684246886433083086663049926232997, 215382389610410475338197708100689466705869805], true]
[59, [887659823945873691335694665461368083190438599, 887659823945873691335694665461368083190438600, 1255340561797968413560325456648720599822541401], true]
[60, [5173660595433557901127734909681545449216398600, 5173660595433557901127734909681545449216398601, 7316660981177400006023755031791634132229378601], true]
[61, [30154303748655473715430714792627904612107953003, 30154303748655473715430714792627904612107953004, 42644625325266431622582204734101084193553730205], true]
[62, [175752161896499284391456553846085882223431319420, 175752161896499284391456553846085882223431319421, 248551090970421189729469473372814871029093002629], true]
[63, [1024358667630340232633308608283887388728479963519, 1024358667630340232633308608283887388728479963520, 1448661920497260706754234635502788141981004285569], true]
[64, [5970399843885542111408395095857238450147448461696, 5970399843885542111408395095857238450147448461697, 8443420432013143050795938339643913980856932710785], true]
[65, [34798040395682912435817061966859543312156210806659, 34798040395682912435817061966859543312156210806660, 49211860671581597598021395402360695743160591979141], true]
[66, [202817842530211932503493976705300021422789816378260, 202817842530211932503493976705300021422789816378261, 286827743597476442537332434074520260478106619164061], true]
[67, [1182109014785588682585146798264940585224582687462903, 1182109014785588682585146798264940585224582687462904, 1671754600913277057625973209044760867125479123005225], true]
[68, [6889836246183320163007386812884343489924706308399160, 6889836246183320163007386812884343489924706308399161, 9743699861882185903218506820194044942274768118867289], true]
[69, [40156908462314332295459174079041120354323655162932059, 40156908462314332295459174079041120354323655162932060, 56790444570379838361685067712119508786523129590198509], true]
[70, [234051614527702673609747657661362378636017224669193196, 234051614527702673609747657661362378636017224669193197, 330998967560396844266891899452523007776864009422323765], true]
[71, [1364152778703901709363026771889133151461779692852227119, 1364152778703901709363026771889133151461779692852227120, 1929203360792001227239666329003018537874660926943744081], true]
[72, [7950865057695707582568412973673436530134660932444169520, 7950865057695707582568412973673436530134660932444169521, 11244221197191610519171106074565588219471101552240140721], true]
[73, [46341037567470343786047451070151486029346185901812790003, 46341037567470343786047451070151486029346185901812790004, 65536123822357661887786970118390510778951948386497100245], true]
[74, [270095360347126355133716293447235479645942454478432570500, 270095360347126355133716293447235479645942454478432570501, 381972521736954360807550714635777476454240588766742460749], true]
[75, [1574231124515287787016250309613261391846308540968782632999, 1574231124515287787016250309613261391846308540968782633000, 2226299006599368502957517317696274347946491584213957664249], true]
[76, [9175291386744600366963785564232332871431908791334263227496, 9175291386744600366963785564232332871431908791334263227497, 12975821517859256656937553191541868611224708916517003524745], true]
[77, [53477517195952314414766463075780735836745144207036796731979, 53477517195952314414766463075780735836745144207036796731980, 75628630100556171438667801831554937319401761914888063484221], true]
[78, [311689811788969286121634992890452082149038956450886517164380, 311689811788969286121634992890452082149038956450886517164381, 440795959085477771975069257797787755305185862572811377380581], true]
[79, [1816661353537863402315043494266931757057488594498282306254303, 1816661353537863402315043494266931757057488594498282306254304, 2569147124412310460411747744955171594511713413521980200799265], true]
[80, [10588278309438211127768625972711138460195892610538807320361440, 10588278309438211127768625972711138460195892610538807320361441, 14974086787388384990495417211933241811765094618559069827415009], true]
[81, [61713008503091403364296712341999899004117867068734561615914339, 61713008503091403364296712341999899004117867068734561615914340, 87275373599917999482560755526644279276078854297832438763690789], true]
[82, [359689772709110209058011648079288255564511309801868562375124596, 359689772709110209058011648079288255564511309801868562375124597, 508678154812119611904869115947932433844708031168435562754729725], true]
[83, [2096425627751569850983773176133729634382949991742476812634833239, 2096425627751569850983773176133729634382949991742476812634833240, 2964793555272799671946653940160950323792169332712780937764687561], true]
[84, [12218863993800308896844627408723089550733188640652992313433874840, 12218863993800308896844627408723089550733188640652992313433874841, 17280083176824678419775054525017769508908307965108250063833395641], true]
[85, [71216758335050283530083991276204807670016181852175477067968415803, 71216758335050283530083991276204807670016181852175477067968415804, 100715705505675270846703673209945666729657678457936719445235686285], true]
[86, [415081686016501392283659320248505756469363902472399870094376619980, 415081686016501392283659320248505756469363902472399870094376619981, 587014149857226946660446984734656230869037762782512066607580722069], true]
[87, [2419273357763958070171871930214829731146167232982223743498291304079, 2419273357763958070171871930214829731146167232982223743498291304080, 3421369193637686409115978235197991718484568898237135680200248646129], true]
[88, [14100558460567247028747572261040472630407639495420942590895371204496, 14100558460567247028747572261040472630407639495420942590895371204497, 19941201011968891508035422426453294080038375626640302014593911154705], true]
[89, [82184077405639524102313561636028006051299669739543431801873935922899, 82184077405639524102313561636028006051299669739543431801873935922900, 116225836878175662639096556323521772761745684861604676407363218282101], true]
[90, [479003905973269897585133797555127563677390378941839648220348244332900, 479003905973269897585133797555127563677390378941839648220348244332901, 677413820257085084326543915514677342490435733542987756429585398537901], true]
[91, [2791839358433979861408489223694737376013042603911494457520215530074503, 2791839358433979861408489223694737376013042603911494457520215530074504, 3948257084664334843320166936764542282180868716396321862170149172945305], true]
[92, [16272032244630609270865801544613296692400865244527127096900944936114120, 16272032244630609270865801544613296692400865244527127096900944936114121, 23012128687728923975594457705072576350594776564834943416591309639133929], true]
[93, [94840354109349675763786320043985042778392148863251268123885454086610219, 94840354109349675763786320043985042778392148863251268123885454086610220, 134124515041709209010246579293670915821387790672613338637377708661858269], true]
[94, [552770092411467445311852118719296959977952027934980481646411779583547196, 552770092411467445311852118719296959977952027934980481646411779583547197, 781734961562526330085885018056952918577731967470845088407674942332015685], true]
[95, [3221780200359454996107326392271796717089320018746631621754585223414672959, 3221780200359454996107326392271796717089320018746631621754585223414672960, 4556285254333448771505063529048046595645004014152457191808671945330235841], true]
[96, [18777911109745262531332106234911483342557968084544809248881099560904490560, 18777911109745262531332106234911483342557968084544809248881099560904490561, 26555976564438166298944496156231326655292292117443898062444356729649399361], true]
[97, [109445686458112120191885311017197103338258488488522223871532012142012270403, 109445686458112120191885311017197103338258488488522223871532012142012270404, 154779574132295549022161913408339913336108748690510931182857468432566160325], true]
[98, [637896207638927458619979759868271136686992962846588533980310973291169131860, 637896207638927458619979759868271136686992962846588533980310973291169131861, 902121468229335127834026984293808153361360200025621689034700453865747562589], true]
[99, [3717931559375452631527993248192429716783699288591008980010333827605002520759, 3717931559375452631527993248192429716783699288591008980010333827605002520760, 5257949235243715217981999992354509006832052451463219203025345254761919215209], true]
[100, [21669693148613788330547979729286307164015202768699465346081691992338845992696, 21669693148613788330547979729286307164015202768699465346081691992338845992697, 30645573943232956180057972969833245887630954508753693529117371074705767728665], true]

160709

Ruby

Numbers n such that 2 * n^2 - 1 is a square(2)

オンライン整数列大辞典の

A001652（http://oeis.org/A001652/list）、

A046090（http://oeis.org/A046090/list）
と比較し、答え合わせしてみる。

また、

23660^2 + 23661^2 = 33461^2

のような関係が成り立つことを確認してみる。

def A001652(n)
  a, b, c = 0, 3, 20
  ary = [a, b, c]
  while ary.size < n + 1
    a, b, c = b, c, 6 * c - b + 2
    ary << c
  end
  ary[0..n]
end

def A046090(n)
  a, b, c = 1, 4, 21
  ary = [a, b, c]
  while ary.size < n + 1
    a, b, c = b, c, 6 * c - b - 2
    ary << c
  end
  ary[0..n]
end

def A001653(n)
  a, b, c = 1, 5, 29
  ary = [a, b, c]
  while ary.size < n
    a, b, c = b, c, 6 * c - b
    ary << c
  end
  ary[0..n - 1]
end

a_ary = A001652(20)
# OEIS A001652のデータ
a_ary0 =
[0,3,20,119,696,4059,23660,137903,803760,4684659,
 27304196,159140519,927538920,5406093003,
 31509019100,183648021599,1070379110496,
 6238626641379,36361380737780,211929657785303,
 1235216565974040]
# 一致の確認
p a_ary == a_ary0

b_ary = A046090(20)
# OEIS A046090のデータ
b_ary0 =
[1,4,21,120,697,4060,23661,137904,803761,4684660,
 27304197,159140520,927538921,5406093004,
 31509019101,183648021600,1070379110497,
 6238626641380,36361380737781,211929657785304,
 1235216565974041]
# 一致の確認
p b_ary == b_ary0

c_ary = A001653(21)
(0..20).each{|i|
  a, b, c = a_ary[i], b_ary[i], c_ary[i]
  p [a, b, c, a * a + b * b == c * c]
}

出力結果
true
true
[0, 1, 1, true]
[3, 4, 5, true]
[20, 21, 29, true]
[119, 120, 169, true]
[696, 697, 985, true]
[4059, 4060, 5741, true]
[23660, 23661, 33461, true]
[137903, 137904, 195025, true]
[803760, 803761, 1136689, true]
[4684659, 4684660, 6625109, true]
[27304196, 27304197, 38613965, true]
[159140519, 159140520, 225058681, true]
[927538920, 927538921, 1311738121, true]
[5406093003, 5406093004, 7645370045, true]
[31509019100, 31509019101, 44560482149, true]
[183648021599, 183648021600, 259717522849, true]
[1070379110496, 1070379110497, 1513744654945, true]
[6238626641379, 6238626641380, 8822750406821, true]
[36361380737780, 36361380737781, 51422757785981, true]
[211929657785303, 211929657785304, 299713796309065, true]
[1235216565974040, 1235216565974041, 1746860020068409, true]

2016年7月6日水曜日

160706

Ruby

Numbers n such that 2 * n^2 - 1 is a square(1)

オンライン整数列大辞典の
A001653（http://oeis.org/A001653/list）
と比較し、答え合わせしてみる。

def A001653(n)
  a, b, c = 1, 5, 29
  ary = [a, b, c]
  while ary.size < n
    a, b, c = b, c, 6 * c - b
    ary << c
  end
  ary[0..n - 1]
end
ary = A001653(23)

# OEIS A001653のデータ
ary0 =
[1,5,29,169,985,5741,33461,195025,1136689,6625109,
 38613965,225058681,1311738121,7645370045,
 44560482149,259717522849,1513744654945,
 8822750406821,51422757785981,299713796309065,
 1746860020068409,10181446324101389,
 59341817924539925]
# 一致の確認
p ary == ary0

2016年7月5日火曜日

160705

Ruby

Numbers n such that n^2 divides A000073(n)(18)

さらに追加した。

require 'matrix'
require 'prime'
def power(a, n, mod)
  return Matrix.I(a.row_size) if n == 0
  m = power(a, n >> 1, mod)
  m = (m * m).map{|i| i % mod}
  return m if n & 1 == 0
  (m * a).map{|i| i % mod}
end
def f(m, n, mod)
  ary0 = Array.new(m, 0)
  ary0[0] = 1
  v = Vector.elements(ary0)
  ary1 = [Array.new(m, 1)]
  (0..m - 2).each{|i|
    ary2 = Array.new(m, 0)
    ary2[i] = 1
    ary1 << ary2
  }
  a = Matrix[*ary1]
  (power(a, n, mod) * v)[m - 1]
end

# チェック用
ary0 = (1..103).to_a
p ary0.select{|i| f(3, i, i * i) == 0}

ary1 =
[1, 103, 112, 2621, 30576, 77168, 694512, 9919728, 24770928, 55638128, 57268848,
 80995824, 1300820976, 2346310512, 5251205232, 18552499056, 18579650544, 46395948144,
 75003063408, 151508024304, 151705178352, 393783442416, 445306972656, 612409425264,
 661705799664, 690597394032, 1080326291184, 2004290097264, 2390491709424, 3249633454704,
 4159129331952, 4394639588976, 5788693393392, 9835507399536, 17740453781232,
 34748830731888, 45490575587184, 48634075801584, 69464048240496, 84106792604016,
 94136324051952, 140275445362416, 140480737763184, 283774529521392, 295624141398768,
 321066327284976, 401344756381296, 589929385294704, 649742749424496, 834059959784688,
 1147042853519472, 1239374962770672, 1293488919021936, 1622497195942896,
 2865640109714928, 4047233853232752, 4412969582247408, 10842222725823216,
 11626271261016048, 11895485160559728, 14314629644266224, 17089245465971952,
 18074507814954864, 33227869932247536, 40929991755739632, 75210784146090096,
 92022858874752624, 95908917873800304, 102207830579832432, 104063341133007984,
 130106162354449008, 154633366617680496, 157532022547321968, 173428661783181168,
 262735909163805168, 387867810981526512, 414670341642905712, 468380548539526896,
 572965815899039472, 635931458878964976, 1104269974879164912, 2477084848488078192,
 2592643640045011056, 3374448626065725936, 3421999174492390128, 3525638794125894768,
 5620544535283252848, 7580469007104944496, 7897007689185289584, 8265492027549395184,
 11569572598512919536, 17411037199801640304, 20225708650600807536, 22280243705728370544,
 24433402788799381104, 30600602388716675952, 39662914773368171376, 42566585957397251568,
 44968380114682747632, 46273400234881183728, 47237823104912150256, 69417208138199581296,
 79331954180061653616, 86739456097414109808, 117883656450575009904,
 165248423718382643184, 194910637942123954032, 286655770361943541104,
 289628295674915569008, 324831883519898327664, 412648089346960796784,
 416760007129145198064, 612587983054488285936, 674698718687141466864,
 991487293596548736624, 1031262448705814528112, 1073164973178900931056,
 1191099622480301400048, 1654313608218370754928, 1684815690741866692464,
 2068297662948675880176, 2475880423595785066224, 2779844031686042276592,
 2975706480688968669552, 4332194534012637447792, 4639579921218170453616,
 4885297534960510218096, 8349385280061365899632, 10527279914585532584304,
 11674117914961365108336, 12142864536348343530096, 12528765133460591044848,
 13619804135800028410608, 14864440254272845397616, 19916982257915926273776,
 23884845720370461201648, 37882752302575312514928, 42496937231276674783728,
 42502071809085835525488, 74288639370518584987248, 79727215498205052186864,
 86670078639932457122544, 98332837230431239987824, 106133531144573215880688,
 145721822991786809874288, 162463001270456627670384, 299891298601436743773936,
 321845956423880619105648, 349873179175936630167408, 500497254754097183187696,
 594972859921905679080048, 655837027552548084258288, 811475656770754999151856,
 874328073121641364048368, 3098529388193008423980144, 9471881824653925103302512,
 21865622854722636847913328, 23466377094971687027000304, 25509893146353453213068784,
 31456345807695430829868528, 44736316034253873830686704, 193741671728874600400181616,
 26608001004934392927781006704, 119675183069386283538046118967250380133556976,
 150846183425306270568198271880911593663365616,
 3196883165332515792151825975972159404507707499888,
 35251093758476397062811685957578349411598247437424,
 38364558984374718487339298289200364704810113751664,
 156640034484488859114452199305585527064381825944944,
 230186599675331184392682948743842783670892365681904,
 390493855725072664250918616237125152488824273117424,
 423011465793699086384763981309949502911648672227312,
 1115948148131925190468155927711505377905679421284336,
 2493686679828617482075738024108623327470662938458736,
 2538209232558963478446482880450818146163592626752368,
 2985096481419036616030510716035806455208685145314544,
 3203631571040413718778235462061295746473425487450992,
 3482612536514512147817884074008728884258200392306032,
 4981913783740522854300801248163060821631867685177584,
 6528154742940086664834048087768207305075326436973552,
 747076430023390282952168060498957959080001657941326832,
 813060098555853408902181748643023329189040740739015152]
p a = ary1.select{|i| f(3, i, i * i) == 0}
a.each{|i| p [i, i.prime_division]}

出力結果
[1, 103]
[1, 103, 112, 2621, 30576, 77168, 694512, 9919728, 24770928, 55638128, 57268848, 80995824, 1300820976, 2346310512, 5251205232, 18552499056, 18579650544, 46395948144, 75003063408, 151508024304, 151705178352, 393783442416, 445306972656, 612409425264, 661705799664, 690597394032, 1080326291184, 2004290097264, 2390491709424, 3249633454704, 4159129331952, 4394639588976, 5788693393392, 9835507399536, 17740453781232, 34748830731888, 45490575587184, 48634075801584, 69464048240496, 84106792604016, 94136324051952, 140275445362416, 140480737763184, 283774529521392, 295624141398768, 321066327284976, 401344756381296, 589929385294704, 649742749424496, 834059959784688, 1147042853519472, 1239374962770672, 1293488919021936, 1622497195942896, 2865640109714928, 4047233853232752, 4412969582247408, 10842222725823216, 11626271261016048, 11895485160559728, 14314629644266224, 17089245465971952, 18074507814954864, 33227869932247536, 40929991755739632, 75210784146090096, 92022858874752624, 95908917873800304, 102207830579832432, 104063341133007984, 130106162354449008, 154633366617680496, 157532022547321968, 173428661783181168, 262735909163805168, 387867810981526512, 414670341642905712, 468380548539526896, 572965815899039472, 635931458878964976, 1104269974879164912, 2477084848488078192, 2592643640045011056, 3374448626065725936, 3421999174492390128, 3525638794125894768, 5620544535283252848, 7580469007104944496, 7897007689185289584, 8265492027549395184, 11569572598512919536, 17411037199801640304, 20225708650600807536, 22280243705728370544, 24433402788799381104, 30600602388716675952, 39662914773368171376, 42566585957397251568, 44968380114682747632, 46273400234881183728, 47237823104912150256, 69417208138199581296, 79331954180061653616, 86739456097414109808, 117883656450575009904, 165248423718382643184, 194910637942123954032, 286655770361943541104, 289628295674915569008, 324831883519898327664, 412648089346960796784, 416760007129145198064, 612587983054488285936, 674698718687141466864, 991487293596548736624, 1031262448705814528112, 1073164973178900931056, 1191099622480301400048, 1654313608218370754928, 1684815690741866692464, 2068297662948675880176, 2475880423595785066224, 2779844031686042276592, 2975706480688968669552, 4332194534012637447792, 4639579921218170453616, 4885297534960510218096, 8349385280061365899632, 10527279914585532584304, 11674117914961365108336, 12142864536348343530096, 12528765133460591044848, 13619804135800028410608, 14864440254272845397616, 19916982257915926273776, 23884845720370461201648, 37882752302575312514928, 42496937231276674783728, 42502071809085835525488, 74288639370518584987248, 79727215498205052186864, 86670078639932457122544, 98332837230431239987824, 106133531144573215880688, 145721822991786809874288, 162463001270456627670384, 299891298601436743773936, 321845956423880619105648, 349873179175936630167408, 500497254754097183187696, 594972859921905679080048, 655837027552548084258288, 811475656770754999151856, 874328073121641364048368, 3098529388193008423980144, 9471881824653925103302512, 21865622854722636847913328, 23466377094971687027000304, 25509893146353453213068784, 31456345807695430829868528, 44736316034253873830686704, 193741671728874600400181616, 26608001004934392927781006704, 119675183069386283538046118967250380133556976, 150846183425306270568198271880911593663365616, 3196883165332515792151825975972159404507707499888, 35251093758476397062811685957578349411598247437424, 38364558984374718487339298289200364704810113751664, 156640034484488859114452199305585527064381825944944, 230186599675331184392682948743842783670892365681904, 390493855725072664250918616237125152488824273117424, 423011465793699086384763981309949502911648672227312, 1115948148131925190468155927711505377905679421284336, 2493686679828617482075738024108623327470662938458736, 2538209232558963478446482880450818146163592626752368, 2985096481419036616030510716035806455208685145314544, 3203631571040413718778235462061295746473425487450992, 3482612536514512147817884074008728884258200392306032, 4981913783740522854300801248163060821631867685177584, 6528154742940086664834048087768207305075326436973552, 747076430023390282952168060498957959080001657941326832, 813060098555853408902181748643023329189040740739015152]
[1, []]
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[2621, [[2621, 1]]]
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[4639579921218170453616, [[2, 4], [3, 2], [7, 1], [13, 1], [757, 1], [1873, 1], [7561, 1], [33026449, 1]]]
[4885297534960510218096, [[2, 4], [3, 1], [7, 2], [13, 1], [883, 1], [10597, 1], [25579, 1], [667549, 1]]]
[8349385280061365899632, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [757, 1], [7561, 1], [2804257, 1]]]
[10527279914585532584304, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [2804257, 1]]]
[11674117914961365108336, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1], [19789009, 1]]]
[12142864536348343530096, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [21193, 1], [667549, 1]]]
[12528765133460591044848, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1], [21237737, 1]]]
[13619804135800028410608, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1], [23087177, 1]]]
[14864440254272845397616, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [93493, 1], [1038409, 1]]]
[19916982257915926273776, [[2, 4], [3, 1], [7, 2], [53, 1], [883, 1], [10597, 1], [25579, 1], [667549, 1]]]
[23884845720370461201648, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [233689, 1], [667549, 1]]]
[37882752302575312514928, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [1873, 1], [7561, 1], [33026449, 1]]]
[42496937231276674783728, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [2804257, 1]]]
[42502071809085835525488, [[2, 4], [3, 2], [7, 2], [13, 1], [757, 1], [883, 1], [667549, 1], [1038409, 1]]]
[74288639370518584987248, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [19789009, 1]]]
[79727215498205052186864, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [21237737, 1]]]
[86670078639932457122544, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [23087177, 1]]]
[98332837230431239987824, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [757, 1], [7561, 1], [33026449, 1]]]
[106133531144573215880688, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [667549, 1], [1038409, 1]]]
[145721822991786809874288, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [254329, 1], [667549, 1]]]
[162463001270456627670384, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [43276897, 1]]]
[299891298601436743773936, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [19789009, 1]]]
[321845956423880619105648, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [21237737, 1]]]
[349873179175936630167408, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [23087177, 1]]]
[500497254754097183187696, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [33026449, 1]]]
[594972859921905679080048, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [667549, 1], [1038409, 1]]]
[655837027552548084258288, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [43276897, 1]]]
[811475656770754999151856, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [757, 1], [883, 1], [7561, 1], [33026449, 1]]]
[874328073121641364048368, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [667549, 1], [1525969, 1]]]
[3098529388193008423980144, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [2804257, 1]]]
[9471881824653925103302512, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [667549, 1], [16531321, 1]]]
[21865622854722636847913328, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [19789009, 1]]]
[23466377094971687027000304, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [21237737, 1]]]
[25509893146353453213068784, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [23087177, 1]]]
[31456345807695430829868528, [[2, 4], [3, 1], [7, 2], [53, 1], [107, 1], [883, 1], [3853, 1], [667549, 1], [1038409, 1]]]
[44736316034253873830686704, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [233689, 1], [667549, 1]]]
[193741671728874600400181616, [[2, 4], [3, 2], [7, 2], [883, 1], [7561, 1], [10597, 1], [254329, 1], [1525969, 1]]]
[26608001004934392927781006704, [[2, 4], [3, 2], [7, 2], [883, 1], [10597, 1], [254329, 1], [1038409, 1], [1525969, 1]]]
[119675183069386283538046118967250380133556976, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [21193, 1], [25579, 1], [46237, 1]]]
[150846183425306270568198271880911593663365616, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1]]]
[3196883165332515792151825975972159404507707499888, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [21193, 1], [25579, 1], [26713, 1], [46237, 1]]]
[35251093758476397062811685957578349411598247437424, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [233689, 1]]]
[38364558984374718487339298289200364704810113751664, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [254329, 1]]]
[156640034484488859114452199305585527064381825944944, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [1038409, 1]]]
[230186599675331184392682948743842783670892365681904, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [1525969, 1]]]
[390493855725072664250918616237125152488824273117424, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [2588689, 1]]]
[423011465793699086384763981309949502911648672227312, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [2804257, 1]]]
[1115948148131925190468155927711505377905679421284336, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [7397921, 1]]]
[2493686679828617482075738024108623327470662938458736, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [16531321, 1]]]
[2538209232558963478446482880450818146163592626752368, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [16826473, 1]]]
[2985096481419036616030510716035806455208685145314544, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [19789009, 1]]]
[3203631571040413718778235462061295746473425487450992, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [21237737, 1]]]
[3482612536514512147817884074008728884258200392306032, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [23087177, 1]]]
[4981913783740522854300801248163060821631867685177584, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [33026449, 1]]]
[6528154742940086664834048087768207305075326436973552, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [43276897, 1]]]
[747076430023390282952168060498957959080001657941326832, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [21193, 1], [25579, 1], [26713, 1], [46237, 1], [233689, 1]]]
[813060098555853408902181748643023329189040740739015152, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [21193, 1], [25579, 1], [26713, 1], [46237, 1], [254329, 1]]]

2016年7月4日月曜日

160704(2)

Ruby

Numbers n such that n^2 divides A000073(n)(17)

さらに追加した。

require 'matrix'
require 'prime'
def power(a, n, mod)
  return Matrix.I(a.row_size) if n == 0
  m = power(a, n >> 1, mod)
  m = (m * m).map{|i| i % mod}
  return m if n & 1 == 0
  (m * a).map{|i| i % mod}
end
def f(m, n, mod)
  ary0 = Array.new(m, 0)
  ary0[0] = 1
  v = Vector.elements(ary0)
  ary1 = [Array.new(m, 1)]
  (0..m - 2).each{|i|
    ary2 = Array.new(m, 0)
    ary2[i] = 1
    ary1 << ary2
  }
  a = Matrix[*ary1]
  (power(a, n, mod) * v)[m - 1]
end

# チェック用
ary0 = (1..103).to_a
p ary0.select{|i| f(3, i, i * i) == 0}

ary1 =
[1, 103, 112, 2621, 30576, 77168, 694512, 9919728, 24770928, 55638128, 57268848,
 80995824, 1300820976, 2346310512, 5251205232, 18552499056, 18579650544, 46395948144,
 75003063408, 151508024304, 151705178352, 393783442416, 445306972656, 612409425264,
 661705799664, 690597394032, 1080326291184, 2004290097264, 2390491709424, 3249633454704,
 4159129331952, 4394639588976, 5788693393392, 9835507399536, 17740453781232,
 34748830731888, 45490575587184, 48634075801584, 69464048240496, 84106792604016,
 94136324051952, 140275445362416, 140480737763184, 283774529521392, 295624141398768,
 321066327284976, 401344756381296, 589929385294704, 649742749424496, 834059959784688,
 1147042853519472, 1239374962770672, 1293488919021936, 1622497195942896,
 2865640109714928, 4047233853232752, 4412969582247408, 10842222725823216,
 11626271261016048, 11895485160559728, 14314629644266224, 17089245465971952,
 18074507814954864, 33227869932247536, 40929991755739632, 75210784146090096,
 92022858874752624, 95908917873800304, 102207830579832432, 104063341133007984,
 130106162354449008, 154633366617680496, 157532022547321968, 173428661783181168,
 262735909163805168, 387867810981526512, 414670341642905712, 468380548539526896,
 572965815899039472, 635931458878964976, 2477084848488078192, 2592643640045011056,
 3374448626065725936, 3421999174492390128, 3525638794125894768, 7580469007104944496,
 7897007689185289584, 8265492027549395184, 11569572598512919536, 17411037199801640304,
 20225708650600807536, 22280243705728370544, 24433402788799381104, 30600602388716675952,
 44968380114682747632, 47237823104912150256, 69417208138199581296, 79331954180061653616,
 117883656450575009904, 165248423718382643184, 194910637942123954032,
 286655770361943541104, 289628295674915569008, 324831883519898327664,
 412648089346960796784, 416760007129145198064, 612587983054488285936,
 674698718687141466864, 991487293596548736624, 1031262448705814528112,
 1073164973178900931056, 1191099622480301400048, 1684815690741866692464,
 2475880423595785066224, 2779844031686042276592, 2975706480688968669552,
 4332194534012637447792, 4639579921218170453616, 4885297534960510218096,
 12142864536348343530096, 14864440254272845397616, 19916982257915926273776,
 23884845720370461201648, 42502071809085835525488, 106133531144573215880688,
 145721822991786809874288, 594972859921905679080048, 874328073121641364048368,
 9471881824653925103302512, 31456345807695430829868528, 44736316034253873830686704,
 193741671728874600400181616, 26608001004934392927781006704,
 119675183069386283538046118967250380133556976,
 150846183425306270568198271880911593663365616,
 3196883165332515792151825975972159404507707499888,
 35251093758476397062811685957578349411598247437424,
 38364558984374718487339298289200364704810113751664,
 156640034484488859114452199305585527064381825944944,
 230186599675331184392682948743842783670892365681904,
 390493855725072664250918616237125152488824273117424,
 423011465793699086384763981309949502911648672227312,
 1115948148131925190468155927711505377905679421284336,
 2493686679828617482075738024108623327470662938458736,
 2538209232558963478446482880450818146163592626752368,
 2985096481419036616030510716035806455208685145314544,
 3203631571040413718778235462061295746473425487450992,
 3482612536514512147817884074008728884258200392306032,
 4981913783740522854300801248163060821631867685177584,
 6528154742940086664834048087768207305075326436973552,
 747076430023390282952168060498957959080001657941326832,
 813060098555853408902181748643023329189040740739015152]
p a = ary1.select{|i| f(3, i, i * i) == 0}
a.each{|i| p [i, i.prime_division]}

出力結果
[1, 103]
[1, 103, 112, 2621, 30576, 77168, 694512, 9919728, 24770928, 55638128, 57268848, 80995824, 1300820976, 2346310512, 5251205232, 18552499056, 18579650544, 46395948144, 75003063408, 151508024304, 151705178352, 393783442416, 445306972656, 612409425264, 661705799664, 690597394032, 1080326291184, 2004290097264, 2390491709424, 3249633454704, 4159129331952, 4394639588976, 5788693393392, 9835507399536, 17740453781232, 34748830731888, 45490575587184, 48634075801584, 69464048240496, 84106792604016, 94136324051952, 140275445362416, 140480737763184, 283774529521392, 295624141398768, 321066327284976, 401344756381296, 589929385294704, 649742749424496, 834059959784688, 1147042853519472, 1239374962770672, 1293488919021936, 1622497195942896, 2865640109714928, 4047233853232752, 4412969582247408, 10842222725823216, 11626271261016048, 11895485160559728, 14314629644266224, 17089245465971952, 18074507814954864, 33227869932247536, 40929991755739632, 75210784146090096, 92022858874752624, 95908917873800304, 102207830579832432, 104063341133007984, 130106162354449008, 154633366617680496, 157532022547321968, 173428661783181168, 262735909163805168, 387867810981526512, 414670341642905712, 468380548539526896, 572965815899039472, 635931458878964976, 2477084848488078192, 2592643640045011056, 3374448626065725936, 3421999174492390128, 3525638794125894768, 7580469007104944496, 7897007689185289584, 8265492027549395184, 11569572598512919536, 17411037199801640304, 20225708650600807536, 22280243705728370544, 24433402788799381104, 30600602388716675952, 44968380114682747632, 47237823104912150256, 69417208138199581296, 79331954180061653616, 117883656450575009904, 165248423718382643184, 194910637942123954032, 286655770361943541104, 289628295674915569008, 324831883519898327664, 412648089346960796784, 416760007129145198064, 612587983054488285936, 674698718687141466864, 991487293596548736624, 1031262448705814528112, 1073164973178900931056, 1191099622480301400048, 1684815690741866692464, 2475880423595785066224, 2779844031686042276592, 2975706480688968669552, 4332194534012637447792, 4639579921218170453616, 4885297534960510218096, 12142864536348343530096, 14864440254272845397616, 19916982257915926273776, 23884845720370461201648, 42502071809085835525488, 106133531144573215880688, 145721822991786809874288, 594972859921905679080048, 874328073121641364048368, 9471881824653925103302512, 31456345807695430829868528, 44736316034253873830686704, 193741671728874600400181616, 26608001004934392927781006704, 119675183069386283538046118967250380133556976, 150846183425306270568198271880911593663365616, 3196883165332515792151825975972159404507707499888, 35251093758476397062811685957578349411598247437424, 38364558984374718487339298289200364704810113751664, 156640034484488859114452199305585527064381825944944, 230186599675331184392682948743842783670892365681904, 390493855725072664250918616237125152488824273117424, 423011465793699086384763981309949502911648672227312, 1115948148131925190468155927711505377905679421284336, 2493686679828617482075738024108623327470662938458736, 2538209232558963478446482880450818146163592626752368, 2985096481419036616030510716035806455208685145314544, 3203631571040413718778235462061295746473425487450992, 3482612536514512147817884074008728884258200392306032, 4981913783740522854300801248163060821631867685177584, 6528154742940086664834048087768207305075326436973552, 747076430023390282952168060498957959080001657941326832, 813060098555853408902181748643023329189040740739015152]
[1, []]
[103, [[103, 1]]]
[112, [[2, 4], [7, 1]]]
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