

A278045


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


8



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
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OFFSET

0,5


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 (c1)/c^(k+1), where c = 1.839286... (A058265) is the tribonacci constant.
The asymptotic mean of this sequence is 1/(c1) = 1.191487... (End)


LINKS

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


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 *)


CROSSREFS

Cf. A278038, A278042, A278043, A278044, A080843, A058265.
Sequence in context: A119900 A328376 A141097 * A096335 A191910 A129503
Adjacent sequences: A278042 A278043 A278044 * A278046 A278047 A278048


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Nov 18 2016


STATUS

approved



