A134126 Indices k such that the (k+1)-st partial sum of primes divided by k is an integer.

1, 2, 4, 7, 10, 50, 130, 328, 651, 4938, 7492, 8083, 12045, 33170, 43138, 61690, 151496, 265056, 953959, 1971358, 5084552, 9372007, 25274899, 34120615, 38684178, 44161681, 415148959, 1294318767, 3955750033, 6484256906, 21755550341, 22058148324

Offset: 1

Author

Enoch Haga, Oct 09 2007

Keywords

• nonn
• more

Comments

The corresponding quotients are given in A134125.

Examples

			The indices k = 3, 5, 6, 8, etc. do not produce integer quotients and do not appear in the sequence.
		

Crossrefs

Cf. A007504, A134125, A134127, A134128, A134129.

Programs

PARI

lista(pmax) = {my(k = 0, s = 2); forprime(p = 3, pmax, k++; s += p; if(!(s % k), print1(k, ", ")));} \\ 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

Such integers k>0 that A007504(k+1) == 0 (mod k).

Extensions

Edited by R. J. Mathar, Apr 17 2009

More terms from Sean A. Irvine, Dec 08 2010

a(27), a(28) from D. S. McNeil, Dec 08 2010

a(29) from Max Alekseyev, Jan 28 2012

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