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A007506 Primes p with property that p divides the sum of all primes <= p.
(Formerly M1554)
9
2, 5, 71, 369119, 415074643 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No others < 29505444491. - Jud McCranie, Jul 08 2000

No other terms < 10^12. - Jon E. Schoenfield, Sep 11 2008

a(6), if exists, is larger than 10^14. - Giovanni Resta, Jan 09 2014

Also primes p with property that p divides 1 plus the sum of all composites < p.  - Vicente Izquierdo Gomez, Aug 05 2014

REFERENCES

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 71, p. 25, Ellipses, Paris 2008.

Harry L. Nelson, Prime Sums, J. Rec. Math., 14 (1981), 205-206.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..5.

C. Rivera, Puzzle

EXAMPLE

For example 2 divides 2, 5 divides 2+3+5, 71 divides 2+3+5+7+. . .+61+67+71, ...

MAPLE

A007506:=proc(q)  local a, n; a:=0;

for n from 1 to q do a:=a+ithprime(n); if gcd(ithprime(n), a)>1 then print(ithprime(n)); fi; od; end:

A007506(10^10); # Paolo P. Lava, Mar 06 2013

MATHEMATICA

sumOfPrimes = 0; Do[ sumOfPrimes += p;  If[ Divisible[ sumOfPrimes, p], Print[p]], {p, Prime /@ Range[23000000]}]  (* Jean-Fran├žois Alcover, Oct 22 2012 *)

Transpose[Module[{nn=23000000, pr}, pr=Prime[Range[nn]]; Select[Thread[ {Accumulate[ pr], pr}], Divisible[#[[1]], #[[2]]]&]]][[2]] (* Harvey P. Dale, Feb 09 2013 *)

PROG

(PARI) s=0; forprime(p=2, 1e9, s+=p; if(s%p==0, print1(p", "))) \\ Charles R Greathouse IV, Jul 22 2013

CROSSREFS

Cf. A024011, A028581, A028582.

Sequence in context: A100009 A167218 A013045 * A042693 A172037 A128297

Adjacent sequences:  A007503 A007504 A007505 * A007507 A007508 A007509

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

Example corrected by Harvey P. Dale, Feb 09 2013

STATUS

approved

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Last modified December 8 17:06 EST 2016. Contains 278946 sequences.