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%I #11 May 11 2023 09:21:05
%S 3,5,11,19,31,233,739,2207,4871,47933,76103,82723,128663,391273,
%T 521041,769423,2036833,3724997,14722933,31957817,87574217,167518933,
%U 478372393,656640899,749613233,861934273,9083114473,29862785453
%N Largest prime in the partials sums of primes in A134125 which have integer averages.
%F 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 a(n)=A000040(1+A134126(n)). - _R. J. Mathar_, Jun 10 2008
%e 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 (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
%Y Cf. A134125, A134128, A134129.
%K nonn
%O 1,1
%A _Enoch Haga_, Oct 09 2007
%E Edited by _R. J. Mathar_, Jun 10 2008
%E More terms from _Nathaniel Johnston_, Apr 30 2011
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