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 A129634 #11 Aug 10 2025 00:48:28
%S A129634 2,1,0,1,1,7,4,1,1,7,3,1,1,3,16,13,1,4,4,1,1,4,4,1,46,3,7,1,2,7,16,2,
%T A129634 13,4,3,1,13,3,4,22,1,16,16,1,1,7,3,1,10,3,7,1,2,7,16,2,1,4,4,13,1,4,
%U A129634 16,1,1,16,4,2,1,16,8,1,10,3,7,1,1,31,7,2,13,4,4,10,1,8,7,13,1,43,16,5,25,16
%N A129634 Least nonnegative m such that T(n) + T(m) is prime, where T(n) = n*(n+1)/2.
%C A129634 What is the simplest proof that this is defined for all nonzero n?
%C A129634 It appears that a(n)<n except for n=0,5,14,24. The graph of A130504 provides evidence that a(n) exists for all n. - _T. D. Noe_, Jun 04 2007
%H A129634 T. D. Noe, <a href="/A129634/b129634.txt">Table of n, a(n) for n = 0..10000</a>
%F A129634 a(n) = Min{m: m*(m+1)/2 + n*(n+1)/2 is prime}. a(n) = Min{m: A000217(m) + A000217(n) is an element of A000040}.
%e A129634 a(6) = 4 because T(4) = 10 is the least triangular number whose sum with T(6) = 21 is prime, since {21+0 = 3*7, 21+3 = 2^3*3, 21+6 = 3^3} are all composite, but 21+10 = 31 is prime.
%t A129634 nn=100; tri=Range[0,nn]Range[nn+1]/2; Table[k=1; While[k<=Length[tri] && !PrimeQ[tri[[k]]+tri[[n]]], k++ ]; If[k<=Length[tri], k-1,0], {n,Length[tri]}] (* _T. D. Noe_, Jun 04 2007 *)
%Y A129634 Cf. A000040, A000217, A129755, A130334.
%Y A129634 Cf. A069003 (for square numbers).
%K A129634 easy,nonn
%O A129634 0,1
%A A129634 _Jonathan Vos Post_, May 31 2007
%E A129634 Corrected and extended by _T. D. Noe_, Jun 04 2007