A103530 a(n) = 2^n - A103529(n).

2, 1, 2, 1, 4, 3, 2, 5, 8, 7, 6, 1, 12, 11, 10, 13, 16, 15, 14, 9, 4, 19, 18, 21, 24, 23, 22, 17, 28, 27, 26, 29, 32, 31, 30, 25, 20, 3, 34, 37, 40, 39, 38, 33, 44, 43, 42, 45, 48, 47, 46, 41, 36, 51, 50, 53, 56, 55, 54, 49, 60, 59, 58, 61, 64, 63, 62, 57

Offset: 1

Author

N. J. A. Sloane, David Applegate and Philippe Deléham, Mar 22 2005

Keywords

• nonn
• easy

Examples

			a(7) = 2^7 - A103529(7) = 128 - 126 = 2.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..1000
• 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.

Programs

Maple

a:=proc(n)local k,t: if(n=1)then return 2:fi: t:= 2^(n-1) + (n-1): for k from 1 to n-1 do if(k = (n-1) mod 2^k)then t:=t-2^k: fi: od: return t: end: seq(a(n),n=1..80); # Nathaniel Johnston, Apr 30 2011

Formula

Also, miraculously, a(n+1) = 2^n - A102371(n) for n >= 1.