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 A134127 #18 Apr 30 2024 01:47:28
%S A134127 3,5,11,19,31,233,739,2207,4871,47933,76103,82723,128663,391273,
%T A134127 521041,769423,2036833,3724997,14722933,31957817,87574217,167518933,
%U A134127 478372393,656640899,749613233,861934273,9083114473,29862785453,95892456511,160534630967,566082728429,574273844491
%N A134127 Largest prime in the partials sums of primes in A134125 which have integer averages.
%C A134127 Add primes to cumulative totals 3 (to 2), 5, 7, 11, 13, 17, 19, etc. But 7, 13, 17 are omitted from the sequence because the sums at counts 3, 5, 6, e.g., do not produce integral quotients.
%F A134127 a(n) = A000040(1+A134126(n)). - _R. J. Mathar_, Jun 10 2008
%e A134127 At a(4), 11 is added to the previous sum 17: 17+11 = 28 and the index count is 4, so 28/4 = 7, which is integral, so 11 is added to the sequence.
%o A134127 (UBASIC) 10 'primes using counters 20 N=3:C=1:R=5:print 2;3,5 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then N=N+2:goto 30 60 A=A+2:O=A 70 if A<=sqrt(N) then 40 80 C=C+1 90 R=R+N:T=R/C:U=R-N 100 if T=int(T) then print C;U;N;R;T:stop 110 N=N+2:goto 30
%o A134127 (PARI) lista(pmax) = {my(k = 0, s = 2); forprime(p = 3, pmax, k++; s += p; if(!(s % k), print1(p, ", ")));} \\ _Amiram Eldar_, Apr 30 2024
%Y A134127 Cf. A000040, A134125, A134128, A134129.
%K A134127 nonn
%O A134127 1,1
%A A134127 _Enoch Haga_, Oct 09 2007
%E A134127 Edited by _R. J. Mathar_, Jun 10 2008
%E A134127 More terms from _Nathaniel Johnston_, Apr 30 2011
%E A134127 a(29)-a(32) from _Amiram Eldar_, Apr 30 2024