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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

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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.

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

(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

More terms from _Benoit Cloitre, _, Mar 29 2005

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David Applegate, Benoit Cloitre, Philippe DELEHAM 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.

David Applegate, Benoit Cloitre, Philippe DELEHAM Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].

David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://www.research.attneilsloane.com/~njas/doc/slopey.pdf">pdf</a>, <a href="http://www.research.attneilsloane.com/~njas/doc/slopey.ps">ps</a>].

_N. J. A. Sloane (njas(AT)research.att.com), _, Mar 24 2005

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