A336018 - OEIS

%I #24 Jan 04 2021 17:51:55

%S 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,

%T 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,

%U 42,45,47,49,52,54,56,59,61,0,1,2,4,5,7,9,10,12,13

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

%H Chai Wah Wu, <a href="/A336018/b336018.txt">Table of n, a(n) for n = 1..10000</a>

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

%F From _Alois P. Heinz_, Jan 04 2021: (Start)

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

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

%p a:= n-> floor(n*log[2](n))-n*ilog2(n):

%p seq(a(n), n=1..80);  # _Alois P. Heinz_, Jan 04 2021

%t a[n_]:=Floor[FractionalPart[Log[2, n]]*n];

%t Table[a[n], {n, 1, 100}]

%o (PARI) a(n) = floor(n*frac(log(n)/log(2))); \\ _Michel Marcus_, Jul 07 2020

%o (Python)

%o def A336018(n):

%o     return len(bin(n**n//(2**((len(bin(n))-3)*n))))-3 # _Chai Wah Wu_, Jul 09 2020

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

%K nonn

%O 1,6

%A _Andres Cicuttin_, Jul 04 2020