A295514 a(n) = 2^bil(n) - bil(n) where bil(0) = 0 and bil(n) = floor(log_2(n)) + 1 for n > 0.

1, 1, 2, 2, 5, 5, 5, 5, 12, 12, 12, 12, 12, 12, 12, 12, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 121, 121, 121

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

From Robert Israel, Dec 03 2017: (Start)

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

a(n) = 4*a(floor(n/2)) - 5*a(floor(n/4)) + 2*a(floor(n/8)) for n >= 4. (End)

Maple

1, seq((2^k-k)$(2^(k-1)), k=1..8); # Robert Israel, Dec 03 2017

Mathematica

a[n_] := 2^IntegerLength[n, 2] - IntegerLength[n, 2];
Table[a[n], {n, 0, 58}]

Crossrefs

Cf. A000325.

Sequence in context: A280511 A200997 A063960 * A025510 A350172 A356387

Adjacent sequences: A295511 A295512 A295513 * A295515 A295516 A295517

Keyword

nonn

Author

Peter Luschny, Dec 02 2017

Status

approved