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

1,1

Comments

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

Links

Table of n, a(n) for n=1..47.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A213650.

Sequence in context: A320724 A259266 A131652 * A185846 A239023 A341718

Adjacent sequences: A213731 A213732 A213733 * A213735 A213736 A213737

Keyword

nonn

Author

Michel Lagneau, Jun 19 2012

Status

approved