A278043 Number of 1's in tribonacci representation of n (cf. A278038).

0, 1, 1, 2, 1, 2, 2, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 2, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 4, 4, 1, 2, 2, 3, 2, 3, 3, 2, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 3, 4, 4, 5, 4, 5, 1, 2, 2, 3, 2, 3, 3, 2, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 4

Offset: 0

Author

N. J. A. Sloane, Nov 18 2016

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A001590, A003726, A007895, A278038, A278042, A278044.

Programs

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] = 0; a[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; DigitCount[Total[2^(s - 1)], 2, 1]]; Array[a, 100, 0] (* Amiram Eldar, Mar 04 2022 *)

Formula

a(n) = A000120(A003726(n+1)). - John Keith, May 23 2022