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 A232570 Numbers k that divide tribonacci(k) (A000073(k)). 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 k such that k divides Fibonacci(k)). 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 MATHEMATICA trib = LinearRecurrence[{1, 1, 1}, {0, 0, 1}, 2000]; Reap[Do[If[Divisible[ trib[[n+1]], n], Print[n]; Sow[n]], {n, 1, Length[trib]-1}]][[2, 1]] (* Jean-François Alcover, Mar 22 2019 *) 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 April 12 10:04 EDT 2024. Contains 371627 sequences. (Running on oeis4.)