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

1,1

Comments

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

Links

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

Example

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.

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&)]]

Prog

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

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).

Sequence in context: A300082 A050010 A316493 * A283759 A261415 A331547

Adjacent sequences: A213647 A213648 A213649 * A213651 A213652 A213653

Keyword

nonn

Author

Michel Lagneau, Jun 17 2012

Status

approved