160320(2)

Ruby

Flint Hills Series(1)

1 / (k^3 * sin(k)^2) を足していくのだが、
k がπ の整数倍に近くなると、sin(k)^2 が0 に非常に近くなり、
和がはね上がるという現象が起こる。

|sin(n)| が単調減少するようなn が
オンライン整数列大辞典の
A046947（http://oeis.org/A046947/list）

に載っている。
このようなn に対し、|sin(n)| を出力してみた。

require "bigdecimal/math"
include BigMath

# OEIS A046947のデータ
ary =
[1,3,22,333,355,103993,104348,208341,312689,
 833719,1146408,4272943,5419351,80143857,165707065,
 245850922,411557987,1068966896,2549491779,
 6167950454,14885392687,21053343141,1783366216531,
 3587785776203]
ary.each{|i| p [i, sin(BigDecimal.new(i), 20).to_s("F")]}

出力結果
[1, "0.8414709848078965066525023216302990004235682182077195"]
[3, "0.14112000805986722210074480280811027873661474040785"]
[22, "-0.008851309290403875921690256815772325189147244386832657"]
[333, "-0.0088211661138858770062190045466562135970129339359410604"]
[355, "-0.00003014435335948844921433028000861068835820914663354479"]
[103993, "-0.00001912933577842375022430719873765367703799149886189756"]
[104348, "-0.00001101501758424055688621168229387695891928328309090004"]
[208341, "0.00000811431819503807720977332778232788556291864705027314544"]
[312689, "0.0000029006993893321110004497107338625217714512342150525465"]
[833719, "0.00000231291941645270150060048012469910428278466225147478845"]
[1146408, "-0.0000005877799728813812324370606128424477196246349423661123"]
[4272943, "-0.000000549579497810490800503139103415385742543507573300321"]
[5419351, "-0.00000003820047507089660191845931583784291327661105143017665"]
[80143857, "-0.000000014772846817965908649924477458170179674217454320598"]
[165707065, "-0.0000000086547814349647927267429647254036859126268764235432929"]
[245850922, "0.00000000611806538300111631429646364527328154581489954216972"]
[411557987, "0.000000002536716051963676479606716437512520433841766355323260286"]
[1068966896, "0.0000000010446332790737633876191107571178922006140748549938843"]
[2549491779, "0.00000000044744949381614970669417348542169260812100547485425011124"]
[6167950454, "0.0000000001497342914414639743903370168443654497673500978170082"]
[14885392687, "0.00000000014798091093322175792677105421503022486546067260839994514"]
[21053343141, "0.000000000001753380508242216463585373307000934397696596409322905"]
[1783366216531, "0.000000000000696948240875574986138551235699323262745413628391514361732419863824"]
[3587785776203, "0.00000000000035948402649106649130828706488939422795851153359998"]