A230404 a(n) = the largest k such that (k+1)! divides 2n; the number of trailing zeros in the factorial base representation of even numbers.

1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1

Offset: 1

Author

Antti Karttunen, Oct 31 2013

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080

Crossrefs

Used to compute A230405 and A219650. See A007623 for factorial base representation.

Analogous sequence for binary system: A001511.

Cf. A019762.

Programs

Scheme

(define (A230404 n) (A230403 (* 2 n)))

Formula

a(n) = A230403(2n) = A055881(2n) - 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*e - 4 = A019762 - 4 = 1.436563... . - Amiram Eldar, Jan 05 2024