OFFSET
1,2
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
EXAMPLE
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.
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 *)
PROG
(PARI) s=0; t=0; for(w=2, 1000000000, if(isprime(w), s=s+w; t=t+1; if(s%w, print(t)), ))
CROSSREFS
KEYWORD
nonn,nice,hard,more
AUTHOR
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
STATUS
approved