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

1,3

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007583, A007814, A122840, A280049.

Sequence in context: A350386 A352550 A348326 * A051907 A178176 A093569

Adjacent sequences: A364210 A364211 A364212 * A364214 A364215 A364216

Keyword

nonn,base,easy

Author

Amiram Eldar, Jul 14 2023

Status

approved