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
Keywords
Examples
tribonacci(256) = 10285895715599251294835119279496333059462348558276025598603904254464 = 256 * 257 * 156339611436029476149609668037091638184921397104146789862048642.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1000 from Alois P. Heinz)
Programs
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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 *)
Comments