A278045 Number of trailing 0's in tribonacci representation of n (cf. A278038).

1, 0, 1, 0, 2, 0, 1, 3, 0, 1, 0, 2, 0, 4, 0, 1, 0, 2, 0, 1, 3, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 3, 0, 1, 0, 2, 0, 4, 0, 1, 0, 2, 0, 1, 6, 0, 1, 0, 2, 0, 1, 3, 0, 1, 0, 2, 0, 4, 0, 1, 0, 2, 0, 1, 3, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 3, 0, 1, 0, 2, 0, 7, 0, 1, 0, 2, 0, 1, 3, 0, 1, 0, 2, 0, 4, 0, 1, 0, 2, 0

Offset: 0

Author

N. J. A. Sloane, Nov 18 2016

Keywords

• nonn
• base

Comments

The number mod 3 of trailing 0's in the tribonacci representation of n >= 1 (this sequence mod 3) is the tribonacci word itself (A080843). - N. J. A. Sloane, Oct 04 2018

The number of trailing 1's in the tribonacci representation of n >= 0 (cf. A278038) is also the tribonacci word itself (A080843).

From Amiram Eldar, Mar 04 2022: (Start)

The asymptotic density of the occurrences of k = 0, 1, 2, ... is (c-1)/c^(k+1), where c = 1.839286... (A058265) is the tribonacci constant.

The asymptotic mean of this sequence is 1/(c-1) = 1.191487... (End)

Links

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

Crossrefs

Cf. A278038, A278042, A278043, A278044, A080843, A058265.

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] = 1; 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]; Min[s] - 1]; Array[a, 100, 0] (* Amiram Eldar, Mar 04 2022 *)