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 A232570 Numbers n such that n divides tribonacci(n) (A000073(n)). 3
 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)). Includes all primes p such that x^3-x^2-x-1 has 3 distinct roots in the field GF(p). - Robert Israel, Feb 07 2018 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 MAPLE with(LinearAlgebra[Modular]): T:= (n, m)-> MatrixPower(m, Mod(m, <<0|1|0>,     <0|0|1>, <1|1|1>>, float[8]), n)[1, 3]: a:= proc(n) option remember; local k; if n=1       then 1 else for k from 1+a(n-1)       while T(k\$2)>0 do od; k fi     end: seq(a(n), n=1..70);  # Alois P. Heinz, Feb 05 2018 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 December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)