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

1,1

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.

Links

Table of n, a(n) for n=1..32.

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A000040, A134125, A134128, A134129.

Sequence in context: A124098 A127453 A092602 * A239519 A329178 A298348

Adjacent sequences: A134124 A134125 A134126 * A134128 A134129 A134130

Keyword

nonn

Author

Enoch Haga, Oct 09 2007

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

Status

approved