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 A228615 #14 Jul 30 2025 07:36:50
%S A228615 1,-1,-1,-1,0,0,-1,1,1,1,-1,0,0,0,-1,-1,1,1,1,-1,2,8,-18,-9,-1,4,0,0,
%T A228615 0,0,0,0,0,0,0,-4096,-4096,64,-20,-125,5,-6,-216,24,152,54872,-106742,
%U A228615 14045,125,-21125,-274625,-274625,10985,-16731,-970299,1804275,1312200,373248,-691488,-192080
%N A228615 Determinant of the n X n matrix with (i,j)-entry equal to 1 or 0 according as 2*(i + j) - 1 and 2*(i + j) + 1 are twin primes or not.
%C A228615 Conjecture: a(n) is nonzero for any n > 35.
%C A228615 Clearly this conjecture implies the twin prime conjecture.
%H A228615 Harvey P. Dale, <a href="/A228615/b228615.txt">Table of n, a(n) for n = 1..500</a> (First 200 terms from Zhi-Wei Sun)
%e A228615 a(1) = 1 since 2*(1 + 1) - 1 = 3 and 2*(1 + 1) + 1 = 5 are twin primes.
%t A228615 a[n_]:=a[n]=Det[Table[If[PrimeQ[2(i+j)-1]&&PrimeQ[2(i+j)+1],1,0],{i,1,n},{j,1,n}]]
%t A228615 Table[a[n],{n,1,20}]
%t A228615 Table[Det[Table[If[AllTrue[2(i+j)+{1,-1},PrimeQ],1,0],{i,k},{j,k}]],{k,60}] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 21 2019 *)
%Y A228615 Cf. A001359, A006512, A069191, A228557, A228591.
%K A228615 sign
%O A228615 1,21
%A A228615 _Zhi-Wei Sun_, Aug 27 2013