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 A360533 #28 Feb 22 2023 12:35:19
%S A360533 1,-1,0,3,4,0,3,-1,4,7,3,8,0,-4,7,-5,4,0,11,3,-1,12,4,-8,3,-5,-9,12,8,
%T A360533 0,3,-5,16,12,-8,-12,11,-1,-9,16,4,0,19,15,7,3,20,-4,-12,-16,19,7,3,
%U A360533 -17,16,4,-8,-12,23,15,11,-9,12,4,0,-8,15,3,-17,-21
%N A360533 a(n) = index of the diagonal of the natural number array, A000027, that includes prime(n). See Comments.
%C A360533 The natural number array, A000027 = (w(n,k)) = (n + (n + k - 2) (n + k - 1)/2), has corner:
%C A360533 1 2 4 7 ...
%C A360533 3 5 8 12 ...
%C A360533 6 9 13 18 ...
%C A360533 10 14 19 25 ...
%C A360533 The indexing of diagonals is given in A191360. Conjecture: Every odd-indexed diagonal contains infinitely many primes.
%e A360533 Prime(1) = 2 is in the diagonal (w(n,n+1)), so a(1) = 1.
%e A360533 Prime(13) = 43 is in the diagonal (w(n,n-4)), so a(7) = -4.
%t A360533 Map[1 + #[[1]] - 2 #[[2]] &[{#[[2]], #[[1]] - ((#[[2]] - 1) + (#[[2]] - 1)^2)/
%t A360533 2} &[{#, Floor[(1 + Sqrt[8 # - 7])/2]}] &[Prime[#]]] &, Range[1000]]
%t A360533 (* _Peter J. C. Moses_, Feb 07 2023 *)
%Y A360533 Cf. A000027, A000040, A185787, A191360.
%K A360533 easy,sign
%O A360533 1,4
%A A360533 _Clark Kimberling_, Feb 10 2023