

A213650


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


3



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
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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,changed


AUTHOR

Michel Lagneau, Jun 17 2012


STATUS

approved



