A336018 a(n) = floor(frac(log_2(n))*n), where frac denotes the fractional part.

0, 0, 1, 0, 1, 3, 5, 0, 1, 3, 5, 7, 9, 11, 13, 0, 1, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 27, 29, 0, 1, 2, 4, 6, 7, 9, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59, 61, 0, 1, 2, 4, 5, 7, 9, 10, 12, 13

Offset: 1

Author

Andres Cicuttin, Jul 04 2020

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000079, A000523, A000195, A336017, A326299, A340301.

Programs

Maple

a:= n-> floor(n*log[2](n))-n*ilog2(n):
seq(a(n), n=1..80);  # Alois P. Heinz, Jan 04 2021

Mathematica

a[n_]:=Floor[FractionalPart[Log[2, n]]*n];
Table[a[n], {n, 1, 100}]

PARI

a(n) = floor(n*frac(log(n)/log(2))); \\ Michel Marcus, Jul 07 2020

Python

def A336018(n):
    return len(bin(n**n//(2**((len(bin(n))-3)*n))))-3 # Chai Wah Wu, Jul 09 2020

Formula

a(n) = floor((log_2(n) - floor(log_2(n)))*n).

From Alois P. Heinz, Jan 04 2021: (Start)

a(n) = A326299(n) - A340301(n).

a(n) = 0 <=> n in { A000079 }. (End)