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%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
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