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

1,6

Links

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

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)

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}]

Prog

(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

Crossrefs

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

Sequence in context: A087676 A291207 A058813 * A132701 A215016 A212394

Adjacent sequences: A336015 A336016 A336017 * A336019 A336020 A336021

Keyword

nonn

Author

Andres Cicuttin, Jul 04 2020

Status

approved