A105023 a(n) = A102370(n) - n. Or, 2*A103185(n).

0, 2, 4, 2, 0, 10, 4, 2, 0, 2, 4, 2, 16, 10, 4, 2, 0, 2, 4, 2, 0, 10, 4, 2, 0, 2, 4, 34, 16, 10, 4, 2, 0, 2, 4, 2, 0, 10, 4, 2, 0, 2, 4, 2, 16, 10, 4, 2, 0, 2, 4, 2, 0, 10, 4, 2, 0, 2, 68, 34, 16, 10, 4, 2, 0, 2, 4, 2, 0, 10, 4, 2, 0, 2, 4, 2, 16, 10, 4, 2, 0, 2, 4, 2, 0, 10, 4, 2, 0, 2, 4, 34, 16, 10, 4

Offset: 0

Author

N. J. A. Sloane, Apr 03 2005

Keywords

• nonn
• base

Comments

When written in base 2 as a right justified table, columns have periods 1, 2, 4, 8, ... - Philippe Deléham, Apr 21 2005

Examples

			Has a natural decomposition into blocks: 0; 2; 4, 2, 0; 10, 4, 2, 0, 2, 4, 2; 16, 10, 4, 2, 0, 2, 4, 2, 0, 10, 4, 2, 0, 2, 4; 34, 16, 10, 4, ... where the leading term in each block is given by A105024.
		

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].
• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

Crossrefs

Cf. A102370, A103185, A105024.

Programs

Maple

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

Formula

a(n) = Sum_{ k >= 1 such that n + k == 0 mod 2^k } 2^k.