|
| |
|
|
A024011
|
|
Numbers k such that the k-th prime divides the sum of the first k primes.
|
|
10
|
| |
|
|
|
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
|
|
|
LINKS
|
Table of n, a(n) for n=1..6.
|
|
|
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
|
Cf. A007506, A028581, A028582, A071089.
Sequence in context: A345328 A203314 A174652 * A229197 A188721 A212996
Adjacent sequences: A024008 A024009 A024010 * A024012 A024013 A024014
|
|
|
KEYWORD
|
nonn,nice,hard,more
|
|
|
AUTHOR
|
G. L. Honaker, Jr.
|
|
|
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
|
| |
|
|
