A364213 The number of trailing 0's in the canonical representation of n as a sum of distinct Jacobsthal numbers (A280049).

0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0

Offset: 1

Author

Amiram Eldar, Jul 14 2023

Keywords

• nonn
• base
• easy

Comments

The even terms of A007583.

This sequence is unbounded. The first position of 2*k is A007583(k) = (2^(2*k+1) + 1)/3.

The asymptotic density of the occurrences of (2*k) in this sequence is 3/4^(k+1).

The asymptotic mean of this sequence is 2/3 and its asymptotic standard deviation is 4/3.

Links

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

Crossrefs

Cf. A007583, A007814, A122840, A280049.

Programs

Mathematica

Select[IntegerExponent[Range[100], 2], EvenQ]

PARI

select(x->!(x%2), vector(100, i, valuation(i, 2)))

Formula

a(n) = A122840(A280049(n)).

a(n) = A007583(A003159(n)).