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

Offset

1,2

Comments

The corresponding quotients are given in A134125.

Links

Table of n, a(n) for n=1..29.

Formula

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

Example

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

Crossrefs

Cf. A134125, A134127, A134128, A134129.

Sequence in context: A034744 A219748 A121352 * A277340 A337490 A333716

Adjacent sequences: A134123 A134124 A134125 * A134127 A134128 A134129

Keyword

nonn

Author

Enoch Haga, Oct 09 2007

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

Status

approved