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 A125130 #25 May 15 2025 11:26:00
%S A125130 2,10,41,129,328,712,1371,2427,4028,6338,9523,13887,19580,26940,36227,
%T A125130 47721,61910,79168,99685,124211,153178,186914,225831,271061,322858,
%U A125130 382038,448869,524451,608914,704204,810459,927883,1057828,1201162
%N A125130 Successive sums of consecutive primes that form a triangular grid.
%H A125130 Paolo Xausa, <a href="/A125130/b125130.txt">Table of n, a(n) for n = 1..1000</a>
%F A125130 a(n) ~ x^2/(2*log(x)-1), where x = prime(n*(n-1)/2+n). For n = 10000, the relative error is about 0.06%.
%F A125130 a(n) = A007504(A000217(n)). - _Andrew Howroyd_, Sep 28 2024
%e A125130 The consecutive primes 2, 3, 5, 7, 11, 13 form the triangular grid
%e A125130 2
%e A125130 3 5
%e A125130 7 11 13
%e A125130 These consecutive primes add up to 41, the third entry in the table.
%t A125130 With[{nmax = 50}, Accumulate[Prime[Range[PolygonalNumber[nmax]]]][[PolygonalNumber[Range[nmax]]]]] (* _Paolo Xausa_, May 15 2025 *)
%o A125130 (PARI) a(n) = sum(x=1, n*(n+1)/2, prime(x))
%Y A125130 Cf. A000217, A007504, A078721.
%Y A125130 Partial sums of A007468.
%K A125130 easy,nonn
%O A125130 1,1
%A A125130 _Cino Hilliard_, Jan 10 2007