A278044 Length of tribonacci representation of n (cf. A278038).

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, 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, 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

Offset

0,3

Comments

For n>=2, n appears A001590(n+2) times. - John Keith, May 23 2022

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..20000

Wolfdieter Lang, The Tribonacci and ABC Representations of Numbers are Equivalent, arXiv preprint arXiv:1810.09787 [math.NT], 2018.

Formula

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

Mathematica

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 *)

Crossrefs

Cf. A278038, A278042, A278043.

Cf. A001590.

Similar to, but strictly different from, A201052.

Sequence in context: A143442 A137300 A201052 * A372475 A255121 A095791

Adjacent sequences: A278041 A278042 A278043 * A278045 A278046 A278047

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 18 2016

Status

approved