A134127 Largest prime in the partials sums of primes in A134125 which have integer averages.

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

Offset: 1

Author

Enoch Haga, Oct 09 2007

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A000040, A134125, A134128, A134129.

Programs

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

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

Formula

a(n) = A000040(1+A134126(n)). - R. J. Mathar, Jun 10 2008

Extensions

Edited by R. J. Mathar, Jun 10 2008

More terms from Nathaniel Johnston, Apr 30 2011

a(29)-a(32) from Amiram Eldar, Apr 30 2024