200307

Crystal


A332954(1)

以下の出力結果から、もっと一般的なことが予想される。

def a(k, m, n)
  return 1 if n == 0
  a = (m..m + n - 1).map{|i| [i]}
  len = 1
  while len < n
    b = Array(Array(Int32)).new
    a.each{|c|
      (m..m + n - 1).each{|num|
        if !c.includes?(num)
          i = c.clone + [num]
          if (i[-2] * (len + k + 1)) > (i[-1] * (len + k))
            b << i
          end
        end
      }
    }
    a = b
    len += 1
  end
  a.size
end

def b(k, m, n)
  return 1 if n == 0
  a = (m..m + n - 1).map{|i| [i]}
  len = 1
  while len < n
    b = Array(Array(Int32)).new
    a.each{|c|
      (m..m + n - 1).each{|num|
        if !c.includes?(num)
          i = c.clone + [num]
          if (i[-2] * (len + k + 1)) >= (i[-1] * (len + k))
            b << i
          end
        end
      }
    }
    a = b
    len += 1
  end
  a.size
end

(0..13).each{|i|
  (0..i + 2).each{|j|
    p a = (1..16).map{|k| a(i, j, k)}
    p b = (0..15).map{|k| b(i, j, k)}
    p [i, j, a == b]
  }
}

出力結果
[1, 1, 1, 2, 3, 6, 9, 19, 30, 60, 108, 222, 388, 874, 1601, 3244]
[1, 1, 1, 2, 3, 6, 9, 19, 30, 60, 108, 222, 388, 874, 1601, 3244]
[0, 0, true]
[1, 1, 2, 3, 6, 9, 19, 30, 60, 108, 222, 388, 874, 1601, 3244, 6437]
[1, 1, 2, 3, 6, 9, 19, 30, 60, 108, 222, 388, 874, 1601, 3244, 6437]
[0, 1, true]
[1, 2, 3, 6, 9, 19, 30, 60, 108, 222, 388, 874, 1601, 3244, 6437, 14056]
[1, 1, 2, 5, 8, 18, 29, 59, 107, 221, 387, 873, 1600, 3243, 6436, 14055]
[0, 2, false]
[1, 1, 1, 1, 2, 3, 5, 8, 13, 21, 38, 64, 116, 216, 405, 714]
[1, 1, 1, 1, 2, 3, 5, 8, 13, 21, 38, 64, 116, 216, 405, 714]
[1, 0, true]
[1, 1, 1, 2, 3, 5, 8, 13, 21, 38, 64, 116, 216, 405, 714, 1444]
[1, 1, 1, 2, 3, 5, 8, 13, 21, 38, 64, 116, 216, 405, 714, 1444]
[1, 1, true]
[1, 1, 2, 3, 5, 8, 13, 21, 38, 64, 116, 216, 405, 714, 1444, 2759]
[1, 1, 2, 3, 5, 8, 13, 21, 38, 64, 116, 216, 405, 714, 1444, 2759]
[1, 2, true]
[1, 2, 3, 5, 8, 13, 21, 38, 64, 116, 216, 405, 714, 1444, 2759, 5376]
[1, 1, 2, 4, 7, 12, 20, 37, 63, 115, 215, 404, 713, 1443, 2758, 5375]
[1, 3, false]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270]
[2, 0, true]
[1, 1, 1, 1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270, 449]
[1, 1, 1, 1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270, 449]
[2, 1, true]
[1, 1, 1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270, 449, 931]
[1, 1, 1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270, 449, 931]
[2, 2, true]
[1, 1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270, 449, 931, 1539]
[1, 1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270, 449, 931, 1539]
[2, 3, true]
[1, 2, 3, 5, 7, 12, 17, 31, 46, 89, 141, 270, 449, 931, 1539, 3098]
[1, 1, 2, 4, 6, 11, 16, 30, 45, 88, 140, 269, 448, 930, 1538, 3097]
[2, 4, false]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111]
[3, 0, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209]
[3, 1, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209, 348]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209, 348]
[3, 2, true]
[1, 1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209, 348, 626]
[1, 1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209, 348, 626]
[3, 3, true]
[1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209, 348, 626, 1089]
[1, 1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209, 348, 626, 1089]
[3, 4, true]
[1, 2, 3, 5, 7, 11, 16, 26, 41, 70, 111, 209, 348, 626, 1089, 2033]
[1, 1, 2, 4, 6, 10, 15, 25, 40, 69, 110, 208, 347, 625, 1088, 2032]
[3, 5, false]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63]
[4, 0, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94]
[4, 1, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171]
[4, 2, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171, 266]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171, 266]
[4, 3, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171, 266, 515]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171, 266, 515]
[4, 4, true]
[1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171, 266, 515, 818]
[1, 1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171, 266, 515, 818]
[4, 5, true]
[1, 2, 3, 5, 7, 11, 15, 25, 35, 63, 94, 171, 266, 515, 818, 1544]
[1, 1, 2, 4, 6, 10, 14, 24, 34, 62, 93, 170, 265, 514, 817, 1543]
[4, 6, false]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34]
[5, 0, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54]
[5, 1, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85]
[5, 2, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145]
[5, 3, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145, 231]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145, 231]
[5, 4, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145, 231, 411]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145, 231, 411]
[5, 5, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145, 231, 411, 657]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145, 231, 411, 657]
[5, 6, true]
[1, 2, 3, 5, 7, 11, 15, 23, 34, 54, 85, 145, 231, 411, 657, 1216]
[1, 1, 2, 4, 6, 10, 14, 22, 33, 53, 84, 144, 230, 410, 656, 1215]
[5, 7, false]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[6, 0, true]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[6, 1, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52]
[6, 2, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73]
[6, 3, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131]
[6, 4, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131, 196]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131, 196]
[6, 5, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131, 196, 356]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131, 196, 356]
[6, 6, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131, 196, 356, 556]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131, 196, 356, 556]
[6, 7, true]
[1, 2, 3, 5, 7, 11, 15, 23, 31, 52, 73, 131, 196, 356, 556, 1013]
[1, 1, 2, 4, 6, 10, 14, 22, 30, 51, 72, 130, 195, 355, 555, 1012]
[6, 8, false]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[7, 0, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[7, 1, true]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[7, 2, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[7, 3, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70]
[7, 4, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111]
[7, 5, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111, 177]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111, 177]
[7, 6, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111, 177, 300]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111, 177, 300]
[7, 7, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111, 177, 300, 481]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111, 177, 300, 481]
[7, 8, true]
[1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 70, 111, 177, 300, 481, 852]
[1, 1, 2, 4, 6, 10, 14, 22, 30, 46, 69, 110, 176, 299, 480, 851]
[7, 9, false]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[8, 0, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[8, 1, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[8, 2, true]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[8, 3, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[8, 4, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[8, 5, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106]
[8, 6, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106, 149]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106, 149]
[8, 7, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106, 149, 269]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106, 149, 269]
[8, 8, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106, 149, 269, 404]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106, 149, 269, 404]
[8, 9, true]
[1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 106, 149, 269, 404, 734]
[1, 1, 2, 4, 6, 10, 14, 22, 30, 46, 62, 105, 148, 268, 403, 733]
[8, 10, false]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[9, 0, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[9, 1, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[9, 2, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[9, 3, true]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[9, 4, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[9, 5, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[9, 6, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[9, 7, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 142]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 142]
[9, 8, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 142, 225]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 142, 225]
[9, 9, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 142, 225, 361]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 142, 225, 361]
[9, 10, true]
[1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 142, 225, 361, 612]
[1, 1, 2, 4, 6, 10, 14, 22, 30, 46, 62, 94, 141, 224, 360, 611]
[9, 11, false]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5]
[10, 0, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[10, 1, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[10, 2, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[10, 3, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[10, 4, true]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[10, 5, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[10, 6, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[10, 7, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[10, 8, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127]
[10, 9, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 214]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 214]
[10, 10, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 214, 301]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 214, 301]
[10, 11, true]
[1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 214, 301, 545]
[1, 1, 2, 4, 6, 10, 14, 22, 30, 46, 62, 94, 126, 213, 300, 544]
[10, 12, false]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3]
[11, 0, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5]
[11, 1, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[11, 2, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[11, 3, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[11, 4, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[11, 5, true]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[11, 6, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[11, 7, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[11, 8, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[11, 9, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127]
[11, 10, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191]
[11, 11, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 286]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 286]
[11, 12, true]
[1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 286, 453]
[1, 1, 2, 4, 6, 10, 14, 22, 30, 46, 62, 94, 126, 190, 285, 452]
[11, 13, false]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]
[12, 0, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3]
[12, 1, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5]
[12, 2, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[12, 3, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[12, 4, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[12, 5, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[12, 6, true]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[12, 7, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[12, 8, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[12, 9, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[12, 10, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127]
[12, 11, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191]
[12, 12, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 255]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 255]
[12, 13, true]
[1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 255, 430]
[1, 1, 2, 4, 6, 10, 14, 22, 30, 46, 62, 94, 126, 190, 254, 429]
[12, 14, false]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[13, 0, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]
[13, 1, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3]
[13, 2, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5]
[13, 3, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7]
[13, 4, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11]
[13, 5, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15]
[13, 6, true]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23]
[13, 7, true]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31]
[13, 8, true]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47]
[13, 9, true]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63]
[13, 10, true]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95]
[13, 11, true]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127]
[1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127]
[13, 12, true]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191]
[1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191]
[13, 13, true]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 255]
[1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 255]
[13, 14, true]
[1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 255, 383]
[1, 1, 2, 4, 6, 10, 14, 22, 30, 46, 62, 94, 126, 190, 254, 382]
[13, 15, false]