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 A102724 #25 Feb 05 2025 22:09:23
%S A102724 5,13,25,43,67,97,133,175,227,287,355,433,517,607,707,819,939,1067,
%T A102724 1205,1349,1501,1663,1835,2021,2219,2423,2633,2849,3071,3311,3569,
%U A102724 3837,4113,4401,4701,5009,5329,5659,5999,6351,6711,7083,7467,7857,8253,8663,9097
%N A102724 Sum of the first n pairs of consecutive primes (for example, a(3) = (2+3) + (3+5) + (5+7) = 25).
%C A102724 Partial sums of A001043.
%H A102724 Harvey P. Dale, <a href="/A102724/b102724.txt">Table of n, a(n) for n = 1..1000</a>
%F A102724 a(n) = 2*Sum_{i=1..n} prime(i) - (2 + prime(n)). - _Alonso del Arte_, Apr 21 2016
%F A102724 a(n) = 3*n*(n-1)+7 for n = 2, ..., 8; cf. A378569. - _M. F. Hasler_, Feb 04 2025
%e A102724 a(1) = 5 = (2+3).
%e A102724 a(2) = 13 = (2+3) + (3+5).
%e A102724 a(3) = 25 = (2+3) + (3+5) + (5+7).
%t A102724 Table[Sum[Prime[i] + Prime[i + 1], {i, n}], {n, 47}] (* _Ray Chandler_, Feb 12 2005 *)
%t A102724 Table[2Sum[Prime[i], {i, n}] - (2 + Prime[n]), {n, 2, 50}] (* _Alonso del Arte_, Apr 26 2016 *)
%t A102724 Accumulate[Total/@Partition[Prime[Range[50]],2,1]] (* _Harvey P. Dale_, Apr 13 2019 *)
%Y A102724 Cf. A001043, A102725, A102729, A378569.
%K A102724 easy,nonn
%O A102724 1,1
%A A102724 _Giovanni Teofilatto_, Feb 07 2005
%E A102724 Edited and extended by _Ray Chandler_, Feb 12 2005
%E A102724 Better definition from _Alonso del Arte_, Apr 26 2016