A340632 a(n) in binary is a run of 1-bits from the most significant 1-bit of n down to the least significant 1-bit of n, inclusive.

0, 1, 2, 3, 4, 7, 6, 7, 8, 15, 14, 15, 12, 15, 14, 15, 16, 31, 30, 31, 28, 31, 30, 31, 24, 31, 30, 31, 28, 31, 30, 31, 32, 63, 62, 63, 60, 63, 62, 63, 56, 63, 62, 63, 60, 63, 62, 63, 48, 63, 62, 63, 60, 63, 62, 63, 56, 63, 62, 63, 60, 63, 62, 63, 64, 127, 126

Offset: 0

Author

Kevin Ryde, Jan 13 2021

Keywords

• nonn
• base
• easy

Examples

			n    = 172 = binary 10101100;
a(n) = 252 = binary 11111100.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A023758 (distinct terms).

Cf. A006519, A062383, A142151.

Programs

PARI

a(n) = if(n, 2<
				

Python

def a(n): return (1<
				

Formula

a(n) = A062383(n) - A006519(n) for n>=1.

a(n) = A003817(n) - A135481(n-1).

a(n) = n + A334045(n) (filling in 0-bits, including n=0 by taking A334045(0)=0).

a(n) = A142151(n-1) + 1.

G.f.: x/(1-x) + Sum_{k>=0} 2^k*x^(2^k)*(1/(1-x) - 1/(1-x^(2^(k+1)))).