A111328 a(0)=1, a(1)=2; a(2n) = 2*a(2n-1)+1; a(2n+1) = a(2n) + x, where x is the least number not yet the difference of two terms.

1, 2, 5, 7, 15, 22, 45, 54, 109, 120, 241, 253, 507, 523, 1047, 1065, 2131, 2150, 4301, 4323, 8647, 8671, 17343, 17368, 34737, 34763, 69527, 69554, 139109, 139137, 278275, 278304, 556609, 556640, 1113281, 1113314, 2226629, 2226663, 4453327

Offset

0,2

Comments

Each positive integer can be represented exactly once as the difference of two terms.

Links

Table of n, a(n) for n=0..38.

Paul Erdõs, Problem E3202, American Mathematical Monthly, 94(1987), 372. [N. Sato, Oct 14 2008]

Example

a(4) = 2*a(3)+1 = 15,
a(5) = a(4)+7 = 22 because 7 is not yet a difference.

Crossrefs

Sequence in context: A306956 A337655 A366175 * A244962 A022629 A032216

Adjacent sequences: A111325 A111326 A111327 * A111329 A111330 A111331

Keyword

easy,nonn

Author

Holger Stephan (stephan(AT)wias-berlin.de), Nov 04 2005

Extensions

Edited by Don Reble, May 16 2006

Definition corrected by Guy P. Srinivasan, Dec 11 2006

Status

approved