A189072 Semiprimes in A007504 (the sum of first n primes).

10, 58, 77, 129, 381, 501, 791, 1371, 1851, 2127, 2427, 2747, 3831, 4227, 4661, 6081, 6338, 7141, 7418, 9206, 9523, 11599, 12718, 15537, 20059, 20546, 21037, 26369, 27517, 29897, 34915, 36227, 45434, 47721, 48494, 49281, 50887, 51698, 52519, 54169, 57547

Offset: 1

Author

Zak Seidov, Apr 16 2011

Keywords

• nonn

Comments

a(n) = A007504(k(n)), values of k(n) = 3, 7, 8, 10, 16, 18, 22, 28, 32, 34, 36, 38, 44, 46, 48, 54, 55, 58, 59, 65, 66, 72, 75, 82, 92, 93, 94, 104, 106, 110, 118, 120, 133, 136, 137, 138, 140, 141, 142, 144, 148, 150, 154, 156, 164, 168, 170, 174, 190, 194, 202, 210, 212, 218, 224, 226, 232, 234, 236, 244, 246, 249, 250, 256, 264, 272, 276, 277, 286, 294, 298, 300.

Intersection of A007504 and A001358. - Robert Israel, Jun 23 2017

Examples

			10 = 2*5 = A007504(3), 58 = 2*29 = A007504(7), 77 = 7*11 = A007504(8).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013918 (primes in A007504).

Cf. A007504, A001358.

Programs

Maple

PS:= ListTools:-PartialSums(select(isprime, [2,seq(i,i=3..10^4,2)])):
select(numtheory:-bigomega = 2, PS); # Robert Israel, Jun 23 2017

Mathematica

semiPrimeQ[n_Integer] := Total[FactorInteger[n]][[2]] == 2; Select[Accumulate[Prime[Range[100]]], semiPrimeQ] (* T. D. Noe, Apr 20 2011 *)
With[{nn=200},Select[Accumulate[Prime[Range[nn]]],PrimeOmega[#]==2&]] (* Harvey P. Dale, Dec 22 2018 *)

PARI

{a=0;s=[];forprime(p=2,10^4,2==bigomega(a=a+p)&s=concat(s,a));s}