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 A069752 #27 Mar 12 2023 14:03:15
%S A069752 2,3,8,15,9,14,48,63,35,44,32,39,77,20,80,255,135,152,75,35,77,230,
%T A069752 183,200,299,324,188,203,144,155,960,351,153,84,224,296,665,246,104,
%U A069752 615,245,258,472,99,414,1034,704,735,1175,374,272,636,1377,539,175,399,551
%N A069752 Smallest k>n such that the triangular number n*(n+1)/2 divides the triangular number k*(k+1)/2.
%C A069752 Note that k <= n^2-1, with equality occurring only if n and n+1 are a prime and a power of 2 (in either order); that is, when n is a Mersenne prime or n+1 is a Fermat prime. - _T. D. Noe_, Apr 08 2011
%H A069752 Zak Seidov, <a href="/A069752/b069752.txt">Table of n, a(n) for n = 1..10000</a>
%t A069752 Clear[k]; Join[{2}, Table[Reduce[k*(k+1) == 0, k, Modulus -> n*(n+1)][[3, 2]], {n, 2, 100}]] (* _T. D. Noe_, Apr 08 2011 *)
%o A069752 (PARI) for(s=1,1000,s1=s*(s+1);n=s+1; while(n*(n+1)%s1>0,n++); print1(n,","); ) \\ _Zak Seidov_, Apr 08 2011
%Y A069752 Cf. A000217, A068084, A188621.
%K A069752 easy,nonn
%O A069752 1,1
%A A069752 _Benoit Cloitre_, May 01 2002