A213734 - OEIS

%I #22 Jan 27 2022 13:04:22

%S 3,7,59,137,277,313,499,563,619,719,787,797,919,937,971,1013,1217,

%T 1283,1373,1409,1439,1451,1621,1747,1789,2207,2237,2267,2393,2417,

%U 2441,2591,2707,2797,2801,2939,2999,3251,3529,3769,3847,4201,4441,4447,4597,4643,4721

%N Primes in A213650.

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

%e 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.

%p 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:

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

%o (PARI) isok(n) = isprime(n) && bigomega(vecsum(primes(n))) == 2; \\ _Michel Marcus_, Sep 18 2017

%Y Cf. A213650.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jun 19 2012