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 A249113 #23 Jan 03 2016 10:44:39
%S A249113 4,5,16,5,11,13,8,6,19,6,12,13,7,9,28,5,11,13,12,17,19,6,11,25,8,6,28,
%T A249113 5,20,37,7,14,19,10,11,34,8,6,40,6,20,25,8,9,31,6,11,25,19,21,19,6,12,
%U A249113 25,16,9,28,5,20,22,7,14,40,9,11,34,19,6,52,17,12
%N A249113 Take n and successively add 1, 2, ..., a(n) until reaching a prime for the third time.
%C A249113 Conjecturally (Hardy & Littlewood conjecture F), a(n) exists for all n. - _Charles R Greathouse IV_, Oct 21 2014
%H A249113 Charles R Greathouse IV, <a href="/A249113/b249113.txt">Table of n, a(n) for n = 1..10000</a>
%F A249113 n+A000217(k) is prime for k=a(n) and exactly two smaller positive values. - _M. F. Hasler_, Oct 21 2014
%e A249113 a(1)=4 because 1+1+2+3+4=11 and exactly two partial sums are prime (2,7).
%e A249113 a(2)=5 because 2+1+2+3+4+5=17 and exactly two partial sums are prime (3,5).
%t A249113 Table[k = 0; Do[k++; While[! PrimeQ[n + Total@ Range@ k], k++], {x, 3}]; k, {n, 71}] (* _Michael De Vlieger_, Jan 03 2016 *)
%o A249113 (PARI) a(n)=my(k,s=3); while(s,if(isprime(n+=k++),s--));k \\ _Charles R Greathouse IV_, Oct 21 2014
%o A249113 (PARI) a(n,s=3)=my(k);until(isprime(n+=k++)&&!s--,);k \\ allows one to get A249112(n) as a(n,2). - _M. F. Hasler_, Oct 21 2014
%Y A249113 Cf. A085415, A249112.
%K A249113 easy,nonn
%O A249113 1,1
%A A249113 _Gil Broussard_, Oct 21 2014