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A024011 Numbers k such that the k-th prime divides the sum of the first k primes. 10
1, 3, 20, 31464, 22096548, 1483892396791177 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 7 02:44 EDT 2022. Contains 355141 sequences. (Running on oeis4.)