A071149 Numbers n such that the sum of the first n odd primes (A071148) is prime; analogous to A013916.

1, 9, 15, 17, 53, 55, 61, 65, 71, 75, 95, 115, 117, 137, 141, 143, 155, 183, 191, 203, 249, 273, 275, 283, 291, 305, 339, 341, 377, 409, 411, 415, 435, 439, 449, 483, 495, 497, 509, 525, 583, 599, 605, 621, 633, 637, 643, 645, 671, 675, 709, 713, 715, 727

Offset: 1

Author

Labos Elemer, May 13 2002

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007504, A013916, A013917, A013918, A065091, A071148, A071150, A089228.

Programs

Maple

Primes:= select(isprime, [seq(2*i+1,i=1..10^4)]):
L:= ListTools:-PartialSums(Primes):
select(i -> isprime(L[i]), [$1..nops(L)]); # Robert Israel, May 19 2015

Mathematica

Position[Accumulate@ Prime@ Range[2, 750], ?(PrimeQ@# &)] // Flatten (* _Robert G. Wilson v, May 19 2015, after Harvey P. Dale in A013916 *)

PARI

s=n=0; forprime(p=3,1e4, n++; if(isprime(s+=p), print1(n", "))) \\ Charles R Greathouse IV, May 13 2015

Formula

a(n) = pi(A071150(n)). - Charles R Greathouse IV, May 13 2015