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%I #22 Mar 30 2021 12:43:36
%S 3,7,8,10,16,18,22,28,32,34,36,38,44,46,48,54,55,58,59,65,66,72,75,82,
%T 92,93,94,104,106,110,118,120,133,136,137,138,140,141,142,144,148,150,
%U 154,156,164,168,170,174,190,194,202,210,212,218,224,226,232,234
%N Numbers k such that the sum of the first k primes is semiprime.
%C Numbers k such that A007504(k) is included in A001358.
%H Amiram Eldar, <a href="/A213650/b213650.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%p 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:
%t Flatten[Position[Accumulate[Prime[Range[300]]],_?(PrimeOmega[#]==2&)]]
%o (PARI) isok(n) = bigomega(vecsum(primes(n))) == 2; \\ _Michel Marcus_, Sep 18 2017
%Y 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).
%K nonn
%O 1,1
%A _Michel Lagneau_, Jun 17 2012
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