A103318 Number of solutions i in range [0,n-1] to i == 0 mod 2^(n-i).

1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 3, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3

Offset: 1

Author

N. J. A. Sloane, Mar 21 2005

Keywords

• nonn

Comments

i=0 is always a solution.

a(n) is the number of 1's in (A103745(n) written in base 2). - Philippe Deléham, Apr 02 2005

Examples

			For n = 11 solutions are i = 0, 8 and 10. Four solutions occur for the first time at n = 2059: they are i = 0, 2048, 2056, 2058. Five solutions occur for the first time at n = 2^2059 + 2059 (see A034797).
		

Links

• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

Crossrefs

For records see A034797. Cf. A103745.

Programs

Maple

f:= proc (n) local t1, l; t1 := 0; for l to n do if `mod`(n-l,2^l) = 0 then t1 := t1+1 end if end do; t1 end proc;

Mathematica

f[n_] := Block[{c = 1, k = Max[1, n - Floor[ Log[2, n] + 2]]}, While[k < n, If[ Mod[k, 2^(n - k)] == 0, c++ ]; k++ ]; c]; Table[ f[n], {n, 105}] (* Robert G. Wilson v, Mar 21 2005 *)

Formula

a(n) = A104234(2^n - n). - Philippe Deléham, Apr 21 2005