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

%I #26 Feb 07 2018 11:55:02

%S 1,256,397,1197,8053,8736,9901,32173,33493,33757,38461,48757,56101,

%T 57073,64153,76561,79693,87517,100608,102217,105253,105601,105913,

%U 105997,107713,108553,110976,116293,123121,131437,138517,143137,147541,151237,156601,171253

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

%C A subsequence of A232570.

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

%p with(LinearAlgebra[Modular]):

%p T:= (n, m)-> MatrixPower(m, Mod(m, <<0|1|0>,

%p <0|0|1>, <1|1|1>>, float[8]), n)[1, 3]:

%p a:= proc(n) option remember; local i, k, ok;

%p if n=1 then 1 else

%p for k from 1+a(n-1) do ok:= true;

%p for i in ifactors(k*(k+1))[2] while ok do

%p ok:= is(T(k, i[1]^i[2])=0)

%p od; if ok then break fi

%p od; k

%p fi

%p end:

%p seq(a(n), n=1..10); # _Alois P. Heinz_, Feb 06 2018

%t 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 Cf. A000073, A217738, A232570, A274518.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Feb 04 2018