A299156 Numbers k such that k*(k+1) divides tribonacci(k) (A000073(k)).

1, 256, 397, 1197, 8053, 8736, 9901, 32173, 33493, 33757, 38461, 48757, 56101, 57073, 64153, 76561, 79693, 87517, 100608, 102217, 105253, 105601, 105913, 105997, 107713, 108553, 110976, 116293, 123121, 131437, 138517, 143137, 147541, 151237, 156601, 171253

Offset

1,2

Comments

A subsequence of A232570.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1000 from Alois P. Heinz)

Example

tribonacci(256) = 10285895715599251294835119279496333059462348558276025598603904254464 = 256 * 257 * 156339611436029476149609668037091638184921397104146789862048642.

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 i, k, ok;
      if n=1 then 1 else
        for k from 1+a(n-1) do ok:= true;
          for i in ifactors(k*(k+1))[2] while ok do
            ok:= is(T(k, i[1]^i[2])=0)
          od; if ok then break fi
        od; k
      fi
    end:
seq(a(n), n=1..10);  # Alois P. Heinz, Feb 06 2018

Mathematica

a = b = 0; c = d = 1; k = 2; lst = {1}; While[k < 171255, If[ Mod[c, k (k + 1)] == 0, AppendTo[lst, k]]; a = b; b = c; c = d; d = a + b + c; k++] (* Robert G. Wilson v, Feb 07 2018 *)

Crossrefs

Cf. A000073, A217738, A232570, A274518.

Sequence in context: A114987 A046310 A115176 * A221259 A223693 A223064

Adjacent sequences: A299153 A299154 A299155 * A299157 A299158 A299159

Keyword

nonn

Author

Seiichi Manyama, Feb 04 2018

Status

approved