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Semiprimes that are the sum of the first n odd primes for some n.
1

%I #8 Sep 24 2019 02:37:36

%S 15,26,39,158,326,566,789,961,1159,1262,1369,1478,1591,1718,1849,2582,

%T 3085,3829,4659,5587,7697,8891,10189,13885,14695,16838,17281,18187,

%U 19111,20057,22546,24131,25798,26938,27515,28102,35566,36886,38919,41739,43199,50885

%N Semiprimes that are the sum of the first n odd primes for some n.

%C The set of semiprimes in A071148.

%C Intersection of A001358 and A071148.

%H Robert Israel, <a href="/A274182/b274182.txt">Table of n, a(n) for n = 1..10000</a>

%e 26 appears in the sequence because 26 = 2*13 that is semiprime. Also, 3+5+7+11 = 26.

%e 158 appears in the sequence because 158 = 2*79 that is semiprime. Also, 3+5+7+11+13+17+19+23+29+31 = 158.

%p P:= select(isprime,[seq(i,i=3..10^4,2)]):

%p select(t -> numtheory:-bigomega(t)=2, ListTools:-PartialSums(P)); # _Robert Israel_, Sep 23 2019

%t Select[a = 0; Table[a = a + Prime[k], {k, 2, 300}], PrimeOmega[#] == 2 &]

%o (PARI) s = 0; forprime(p=3, 1e4, s + = p; if (bigomega(s)==2, print1(s, ", ")))

%Y Cf. A001358, A071148, A189072, A274120.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Jun 12 2016