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A232570 Numbers n such that n divides tribonacci(n) (A000073(n)). 2
1, 8, 16, 19, 32, 47, 53, 64, 103, 112, 128, 144, 155, 163, 192, 199, 208, 221, 224, 256, 257, 269, 272, 299, 311, 368, 397, 401, 419, 421, 448, 499, 512, 587, 599, 617, 640, 683, 757, 768, 773, 784, 863, 883, 896, 907, 911, 929, 936, 991, 1021, 1024 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inspired by A023172 (numbers n such that n divides Fibonacci(n)).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

PROG

(Ruby)

require 'matrix'

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)

  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]

  mod = n

  (power(a, n, mod) * v)[m - 1]

end

def a(n)

  (1..n).select{|i| f(3, i) == 0}

end

CROSSREFS

Cf. A000073, A023172.

Sequence in context: A232724 A260409 A257509 * A029522 A033309 A114435

Adjacent sequences:  A232567 A232568 A232569 * A232571 A232572 A232573

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 17 2016

STATUS

approved

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Last modified July 25 20:37 EDT 2017. Contains 289797 sequences.