A213650 Numbers k such that the sum of the first k primes is semiprime.

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

Offset: 1

Author

Michel Lagneau, Jun 17 2012

Keywords

• nonn

Comments

Numbers k such that A007504(k) is included in A001358.

Examples

			8 is in the sequence because the sum of the first 8 primes is  2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 = 7*11, which is semiprime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A007504, A013916, A092189 (numbers n such that sum of first n semiprimes is a semiprime), A092190 (semiprimes that are the sum of first n semiprimes for some n), A180152 (numbers n such that the sum of the first n semiprimes is a prime).

Programs

Maple

with(numtheory): for n from 1 to 500 do:s:=sum(‘ithprime(k)’, ’k’=1..n):if bigomega(s)=2 then printf(`%d, `, n):else fi:od:

Mathematica

Flatten[Position[Accumulate[Prime[Range[300]]],_?(PrimeOmega[#]==2&)]]

PARI

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