A213734 Primes in A213650.

3, 7, 59, 137, 277, 313, 499, 563, 619, 719, 787, 797, 919, 937, 971, 1013, 1217, 1283, 1373, 1409, 1439, 1451, 1621, 1747, 1789, 2207, 2237, 2267, 2393, 2417, 2441, 2591, 2707, 2797, 2801, 2939, 2999, 3251, 3529, 3769, 3847, 4201, 4441, 4447, 4597, 4643, 4721

Offset: 1

Author

Michel Lagneau, Jun 19 2012

Keywords

• nonn

Comments

Primes p such that the sum of the first p primes is semiprime.

Examples

			7 is in the sequence because the sum of the first 7 primes is 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58 = 2*29, which is semiprime.
		

Crossrefs

Cf. A213650.

Programs

Maple

with(numtheory): for n from 1 to 10000 do:s:=sum(‘ithprime(k)’, ’k’=1..n):if bigomega(s)=2 and type(n,prime)=true then printf(`%d, `, n):else fi:od:

Mathematica

Select[Flatten[Position[If[PrimeOmega[#]==2,1,0]&/@Accumulate[ Prime[ Range[ 5000]]],1]],PrimeQ] (* Harvey P. Dale, Jan 27 2022 *)

PARI

isok(n) = isprime(n) && bigomega(vecsum(primes(n))) == 2; \\ Michel Marcus, Sep 18 2017