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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
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
Sequence in context: A232724 A260409 A257509 * A029522 A033309 A114435
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.)