A046820 Number of 1's in binary expansion of 5n.

0, 2, 2, 4, 2, 3, 4, 3, 2, 4, 3, 5, 4, 2, 3, 4, 2, 4, 4, 6, 3, 4, 5, 5, 4, 6, 2, 4, 3, 3, 4, 5, 2, 4, 4, 6, 4, 5, 6, 4, 3, 5, 4, 6, 5, 4, 5, 6, 4, 6, 6, 8, 2, 3, 4, 4, 3, 5, 3, 5, 4, 4, 5, 6, 2, 4, 4, 6, 4, 5, 6, 5, 4, 6, 5, 7, 6, 3, 4, 5, 3, 5, 5, 7, 4, 5, 6, 6, 5, 7, 4, 6, 5

Offset

0,2

Comments

a(n) is also the largest integer such that 2^a(n) divides binomial(10n, 5n). - Benoit Cloitre, Mar 27 2002

Links

Indranil Ghosh, Table of n, a(n) for n = 0..10000

Michael Gilleland, Some Self-Similar Integer Sequences.

Formula

a(n) = floor(log(gcd(binomial(10*n, 5*n), 2^floor(log(binomial(10*n, 5*n))/log(2))))/log(2)). - Benoit Cloitre, Mar 27 2002

a(n) = A000120(5*n). - Indranil Ghosh, Jan 18 2017

Example

For n = 10, 5*n = 50 = 110010_2, having 3 1's. So, a(10) = 3. - Indranil Ghosh, Jan 18 2017

Mathematica

a[n_] := DigitCount[5*n, 2, 1]; Array[a, 100, 0] (* Amiram Eldar, Jul 18 2023 *)

Prog

(Python)
def A046820(n):
....return bin(5*n)[2:].count("1") # Indranil Ghosh, Jan 18 2017
(PARI) a(n) = hammingweight(5*n); \\ Michel Marcus, Aug 19 2018

Crossrefs

Cf. A000120.

Sequence in context: A061338 A135714 A103274 * A356878 A043262 A130860

Adjacent sequences: A046817 A046818 A046819 * A046821 A046822 A046823

Keyword

nonn,base

Author

N. J. A. Sloane

Status

approved