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

0,3

Links

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

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)))).

Example

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

Prog

(PARI) a(n) = if(n, 2<<logint(n, 2) - 1<<valuation(n, 2), 0);
(Python) def a(n): return (1<<n.bit_length()) - (n&-n) if n else 0

Crossrefs

Cf. A023758 (distinct terms).

Cf. A006519, A062383, A142151.

Sequence in context: A265363 A319651 A373185 * A074846 A120225 A247798

Adjacent sequences: A340629 A340630 A340631 * A340633 A340634 A340635

Keyword

nonn,base,easy

Author

Kevin Ryde, Jan 13 2021

Status

approved