login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Length of tribonacci representation of n (cf. A278038).
5

%I #28 Jul 07 2022 02:31:05

%S 1,1,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,

%T 6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,

%U 7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

%N Length of tribonacci representation of n (cf. A278038).

%C For n>=2, n appears A001590(n+2) times. - _John Keith_, May 23 2022

%H N. J. A. Sloane, <a href="/A278044/b278044.txt">Table of n, a(n) for n = 0..20000</a>

%H Wolfdieter Lang, <a href="https://arxiv.org/abs/1810.09787">The Tribonacci and ABC Representations of Numbers are Equivalent</a>, arXiv preprint arXiv:1810.09787 [math.NT], 2018.

%F a(n) = A278042(n) + A278043(n).

%t t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; a[0] = 1; a[n_] := Module[{k = 1}, While[t[k] <= n, k++]; k - 1]; Array[a, 100, 0] (* _Amiram Eldar_, Mar 04 2022 *)

%Y Cf. A278038, A278042, A278043.

%Y Cf. A001590.

%Y Similar to, but strictly different from, A201052.

%K nonn,base

%O 0,3

%A _N. J. A. Sloane_, Nov 18 2016