cp's OEIS Frontend

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.

%I A103122 #16 Apr 18 2022 18:19:12
%S A103122 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,
%T A103122 22,25,12,-5,26,21,32,31,30,33,36,35,34,29,40,39,38,41,28,43,42,37,48,
%U A103122 47,46,49,52,51,50,45,56,55,54,57,44,27,-6,53,64,63,62,65,68
%N 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.
%C A103122 A 1-1 map from the nonnegative integers to all integers.
%C A103122 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
%H A103122 David Applegate, Benoit Cloitre, Philippe 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>].
%H A103122 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.
%o A103122 (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
%K A103122 sign,base
%O A103122 0,3
%A A103122 _N. J. A. Sloane_, Mar 24 2005
%E A103122 More terms from _Benoit Cloitre_, Mar 29 2005