A364377 The number of trailing 0's in the representation of n in Jacobsthal greedy base (A265747).

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

Offset: 1

Author

Amiram Eldar, Jul 21 2023

Keywords

• nonn
• base

Comments

The first position of k, for k = 0, 1, 2, ..., is A001045(k+2).

The asymptotic density of the occurrences of 2*k is 9/4^(k+2), and of 2*k+1 is 3/4^(k+2), both for k >= 0.

The asymptotic mean of this sequence is 11/12, and its asymptotic standard deviation is sqrt(283)/12.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001045, A265747, A324477.

Programs

Mathematica

a[n_] := IntegerExponent[A265747[n], 10]; Array[a, 100] (* using A265747[n] *)

PARI

a(n) = valuation(A265747(n), 10); \\ using A265747(n)