A024011 Numbers k such that the k-th prime divides the sum of the first k primes.

1, 3, 20, 31464, 22096548, 1483892396791177

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• nonn
• nice
• hard
• more

Comments

a(6) > pi(10^12) = 37607912018. - Jon E. Schoenfield, Sep 11 2008

a(6) > pi(10^14) = 3204941750802. - Giovanni Resta, Jan 09 2014

a(7) > 6.5*10^15. - Paul W. Dyson, Sep 27 2022

Examples

			The third prime, 5, divides 2 + 3 + 5 = 10, so 3 is in the sequence.
2 + 3 + 5 + 7 = 17, which is not divisible by the fourth prime, 7, so 4 is not in the sequence.
		

Crossrefs

Cf. A007506, A028581, A028582, A071089.

Programs

Mathematica

s = 0; For[i = 1, i <= 5 * 10^7, i++, s = s + Prime[i]; If[Mod[s, Prime[i + 1]] == 0, Print[i + 1]]]
With[{prs = Prime[Range[221000000]]}, PrimePi /@ Transpose[Select[ Thread[ {Accumulate[prs], prs}], Divisible[#[[1]], #[[2]]] &]][[2]]] (* Harvey P. Dale, Jul 23 2013 *)
nMax = 50000; primeSums = Accumulate[Prime[Range[nMax]]]; Select[Range[nMax], Divisible[primeSums[[#]], Prime[#]] &] (* Alonso del Arte, Nov 11 2019 *)

PARI

s=0; t=0; for(w=2,1000000000,if(isprime(w),s=s+w; t=t+1; if(s%w,print(t)),))

Extensions

a(5) from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 14 2000

a(6) from Paul W. Dyson, Apr 16 2022