This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352931 #12 May 04 2022 14:29:28
%S A352931 0,1,-1,1,-1,1,-1,3,-1,3,-2,2,4,-4,4,-4,6,-3,3,1,-5,3,-5,5,-5,1,-1,3,
%T A352931 -5,5,1,5,-5,-1,3,5,-7,5,-5,-1,3,5,-7,5,-5,5,-1,-3,3,5,-9,1,-5,5,-5,1,
%U A352931 -1,3,-5,5,-3,1,-1,3,-5,5,-3,1,-1,3,-5,7,-3,7,-1,1,-5,5,-4,2,4,-6,4,-4,4,-8,8,-4,8,-4,0,-4,0,-2,4,-2,4,-8,4,-4,6,-4
%N A352931 a(n) = A093714(n) - n.
%C A352931 From _Michael De Vlieger_, May 04 2022: (Start)
%C A352931 Zeros in this sequence correspond to fixed points in A093714.
%C A352931 Sequence exhibits intervals where terms have same parity. Parity changes when a run of odd terms in A093714 with even run length occurs. These runs begin with A093714(A351498(k)). Conjecture: the last parity change begins with a(1036044) = -9. (End)
%C A352931 Rival conjecture: The parity changes infinitely often. This would imply that A352932 contains infinitely many terms. - _N. J. A. Sloane_, May 04 2022
%H A352931 N. J. A. Sloane, <a href="/A352931/b352931.txt">Table of n, a(n) for n = 1..10000</a>
%H A352931 Michael De Vlieger, <a href="/A352931/a352931.png">Scatterplot of a(n)</a>, n = 1..2^20, logarithmic along the x-axis, showing even terms in red and odd in blue, accentuating zeros that are confined to even-term intervals, annotating positive and negative records, and labeling the last term a(k) in parity intervals, with k in A351498.
%t A352931 nn = 120; c = {1}; s = 0; a[1] = j = 1; u = 2; Do[k = u; While[Nand[FreeQ[c, k], CoprimeQ[j, k], k != j + 1], k++]; j = k; AppendTo[c, k]; a[i] = k - i; If[k == u, While[MemberQ[c, u], u++]; c = DeleteCases[c, _?(# < u &)]], {i, 2, nn}], Array[a, nn] (* _Michael De Vlieger_, May 04 2022 *)
%Y A352931 Cf. A093714, A351498, A352932.
%K A352931 sign
%O A352931 1,8
%A A352931 _N. J. A. Sloane_, May 04 2022