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%I #13 Sep 08 2022 08:45:23
%S 2,4,5,8,10,12,13,14,15,17,18,19,23,28,31,32,39,44,48,49,50,53,54,55,
%T 57,58,60,63,64,68,69,71,76,78,81,82,84,85,86,89,90,91,104,108,111,
%U 112,113,116,118,120,122,126,127,129,134,138,141,143,144,147,150,157,159,163
%N Numbers n such that 2*n^2 + 1 is a semiprime.
%C Primes in this sequence include: 2, 5, 13, 17, 19, 23, 31, 53, 71, 89, 113, 127, 157, 159, 163, 167, 181, 197, 229. Semiprimes in this sequence include: 4, 10, 14, 15, 39, 49, 55, 57, 58, 69, 82, 85, 86, 91, 111, 118, 122, 129, 134, 141, 143, 166, 183, 185, 215, 217, 221, 249. - _Jonathan Vos Post_, Nov 12 2005
%H Vincenzo Librandi, <a href="/A112777/b112777.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = Sqrt(A111350(n)).
%t Select[Range[165], Plus @@ Last /@ FactorInteger[2#^2 + 1] == 2 &]
%o (Magma) IsSemiprime:=func<n | &+[k[2]: k in Factorization(n)] eq 2>; [n: n in [2..170] | IsSemiprime(2*n^2+1)]; // _Vincenzo Librandi_, Sep 23 2012
%Y Cf. A111350, A111351.
%K nonn,easy
%O 1,1
%A _Ray Chandler_, Nov 10 2005
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