A103122 Define a 1-1 correspondence between the integers Z and the nonnegative integers N by f(n) = A102370(n) if n >= 0, f(n) = A102371(-n) if n < 0; sequence gives a(n) = f^(-1)(n) for n >= 0.

0, -1, -2, 1, 4, 3, 2, -3, 8, 7, 6, 9, -4, 11, 10, 5, 16, 15, 14, 17, 20, 19, 18, 13, 24, 23, 22, 25, 12, -5, 26, 21, 32, 31, 30, 33, 36, 35, 34, 29, 40, 39, 38, 41, 28, 43, 42, 37, 48, 47, 46, 49, 52, 51, 50, 45, 56, 55, 54, 57, 44, 27, -6, 53, 64, 63, 62, 65, 68

Offset: 0

Author

N. J. A. Sloane, Mar 24 2005

Keywords

• sign
• base

Comments

A 1-1 map from the nonnegative integers to all integers.

Simply stated: a(n) = index of n in A102370 if it is a member, else minus its index in the complement A102371. - M. F. Hasler, Apr 14 2022

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.

Programs

PARI

A103122(n)=if(n<0,0,s=-n;while(abs(if(sign(s)+1,2^s-1/2-1/2*sum(k=0,s,(-1)^floor((s+k)/2^k)*2^k),2^(-s-1)-1/2+1/2*sum(k=0,-s-1,(-1)^floor((-s-1-k)/2^k)*2^k))-n)>0,s++);s) \\ Benoit Cloitre, Mar 29 2005

Extensions

More terms from Benoit Cloitre, Mar 29 2005