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A134127
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Largest prime in the partials sums of primes in A134125 which have integer averages.
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5
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3, 5, 11, 19, 31, 233, 739, 2207, 4871, 47933, 76103, 82723, 128663, 391273, 521041, 769423, 2036833, 3724997, 14722933, 31957817, 87574217, 167518933, 478372393, 656640899, 749613233, 861934273, 9083114473, 29862785453, 95892456511, 160534630967, 566082728429, 574273844491
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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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.
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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