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A368671 For any k >= 0, let P(k) = A368357(k) and P(-k) = A368358(k); for any n > 0, a(n) is the unique k such that P(k) = n.

%I A368671 #19 Dec 23 2024 02:26:06
%S A368671 0,1,2,-1,-3,-2,-4,3,7,5,9,4,8,6,10,-5,-13,-9,-17,-7,-15,-11,-19,-6,
%T A368671 -14,-10,-18,-8,-16,-12,-20,11,27,19,35,15,31,23,39,13,29,21,37,17,33,
%U A368671 25,41,12,28,20,36,16,32,24,40,14,30,22,38,18,34,26,42,-21
%N A368671 For any k >= 0, let P(k) = A368357(k) and P(-k) = A368358(k); for any n > 0, a(n) is the unique k such that P(k) = n.
%C A368671 This sequence is a bijection from the positive integers to the integers (Z).
%H A368671 Rémy Sigrist, <a href="/A368671/b368671.txt">Table of n, a(n) for n = 1..8191</a>
%H A368671 Rémy Sigrist, <a href="/A368671/a368671.gp.txt">PARI program</a>
%F A368671 Conjecture: a(n) = (-1)^(L(n)+1)*(A001045(L(n)+2) - A036044(n)/2 - 1) for n > 0 where L(n) = A000523(n). - _Mikhail Kurkov_, Dec 13 2024
%e A368671 P(2) = A368357(2) = 3, so a(3) = 2.
%e A368671 P(-4) = A368358(4) = 7, so a(7) = -4.
%o A368671 (PARI) \\ See Links section.
%Y A368671 Cf. A368357, A368358.
%K A368671 sign,look
%O A368671 1,3
%A A368671 _Rémy Sigrist_, Jan 02 2024