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 A364695 #21 Aug 07 2023 10:07:21
%S A364695 3,5,7,9,10,11,13,15,16,18,19,20,21,23,24,25,26,27,28,29,30,31,32,34,
%T A364695 35,36,37,39,40,42,44,46,47,49,51,52,53,54,56,57,62,68,70,72,74,75,76,
%U A364695 77,78,79,80,82,83,84,85,86,87,88,90,91,92,97,99,103,105,106
%N A364695 Positive integers k such that the sum of the first k primes is a polygonal number of order greater than 2 (A090466).
%H A364695 Paolo Xausa, <a href="/A364695/b364695.txt">Table of n, a(n) for n = 1..10000</a>
%H A364695 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>.
%H A364695 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%e A364695 5 is a term because the sum of the first 5 primes (2 + 3 + 5 + 7 = 28) is a triangular number.
%e A364695 7 is a term because the sum of the first 7 primes (2 + 3 + 5 + 7 + 11 + 13 = 58) is an octagonal number.
%t A364695 A364693Q[n_]:=With[{d=Divisors[2n]},Catch[For[i=3,i<Length[d]-1,i++,If[Divisible[2n/d[[i]]-2,d[[i]]-1],Throw[True]]];False]]; (* After _Jianing Song_ in A090466 *)
%t A364695 A364695list[kmax_]:=Flatten[Position[Map[A364693Q,Accumulate[Prime[Range[kmax]]]],True]];A364695list[100]
%o A364695 (PARI) isok(k) = my(s = sum(i=1, k, prime(i))); for (j=3, s-1, if (ispolygonal(s, j), return(1))); \\ _Michel Marcus_, Aug 03 2023
%Y A364695 Cf. A007504, A033997, A090466, A175133, A364693, A364694, A364696.
%K A364695 nonn
%O A364695 1,1
%A A364695 _Paolo Xausa_, Aug 03 2023