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

%I A299156 #26 Feb 07 2018 11:55:02
%S A299156 1,256,397,1197,8053,8736,9901,32173,33493,33757,38461,48757,56101,
%T A299156 57073,64153,76561,79693,87517,100608,102217,105253,105601,105913,
%U A299156 105997,107713,108553,110976,116293,123121,131437,138517,143137,147541,151237,156601,171253
%N A299156 Numbers k such that k*(k+1) divides tribonacci(k) (A000073(k)).
%C A299156 A subsequence of A232570.
%H A299156 Chai Wah Wu, <a href="/A299156/b299156.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..1000 from Alois P. Heinz)
%e A299156 tribonacci(256) = 10285895715599251294835119279496333059462348558276025598603904254464 = 256 * 257 * 156339611436029476149609668037091638184921397104146789862048642.
%p A299156 with(LinearAlgebra[Modular]):
%p A299156 T:= (n, m)-> MatrixPower(m, Mod(m, <<0|1|0>,
%p A299156     <0|0|1>, <1|1|1>>, float[8]), n)[1, 3]:
%p A299156 a:= proc(n) option remember; local i, k, ok;
%p A299156       if n=1 then 1 else
%p A299156         for k from 1+a(n-1) do ok:= true;
%p A299156           for i in ifactors(k*(k+1))[2] while ok do
%p A299156             ok:= is(T(k, i[1]^i[2])=0)
%p A299156           od; if ok then break fi
%p A299156         od; k
%p A299156       fi
%p A299156     end:
%p A299156 seq(a(n), n=1..10);  # _Alois P. Heinz_, Feb 06 2018
%t A299156 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 *)
%Y A299156 Cf. A000073, A217738, A232570, A274518.
%K A299156 nonn
%O A299156 1,2
%A A299156 _Seiichi Manyama_, Feb 04 2018