A072376 a(n) = a(floor(n/2)) + a(floor(n/4)) + a(floor(n/8)) + ... starting with a(0)=0 and a(1)=1.

0, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32

Offset: 0

Author

Henry Bottomley, Jul 19 2002

Keywords

• easy
• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A011782, A022825, A053644, A062383.

Programs

Mathematica

lim = 100; CoefficientList[Series[1/(2 - 2 x) (2 x - x^2 + Sum[ 2^(k - 1) x^2^k, {k, Floor@ Log2@ lim}]), {x, 0, lim}], x] (* Michael De Vlieger, Jan 26 2016 *)

PARI

a(n)=if(n<2, return(n)); 2^logint(n\2,2) \\ Charles R Greathouse IV, Jan 26 2016

Python

def A072376(n): return n if n < 2 else 1 << n.bit_length()-2 # Chai Wah Wu, Jun 30 2022

Formula

For n > 1: a(n) = msb(n)/2 = 2^floor(log_2(n)-1) = 2*a(floor(n/2)).

G.f.: 1/(2-2x) * (2x-x^2 + Sum_{k>=1} 2^(k-1)*x^2^k). - Ralf Stephan, Apr 18 2003