A112777 Numbers n such that 2*n^2 + 1 is a semiprime.

2, 4, 5, 8, 10, 12, 13, 14, 15, 17, 18, 19, 23, 28, 31, 32, 39, 44, 48, 49, 50, 53, 54, 55, 57, 58, 60, 63, 64, 68, 69, 71, 76, 78, 81, 82, 84, 85, 86, 89, 90, 91, 104, 108, 111, 112, 113, 116, 118, 120, 122, 126, 127, 129, 134, 138, 141, 143, 144, 147, 150, 157, 159, 163

Offset

1,1

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Formula

a(n) = Sqrt(A111350(n)).

Mathematica

Select[Range[165], Plus @@ Last /@ FactorInteger[2#^2 + 1] == 2 &]

Prog

(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

Crossrefs

Cf. A111350, A111351.

Sequence in context: A306073 A018457 A046809 * A188972 A047612 A123886

Adjacent sequences: A112774 A112775 A112776 * A112778 A112779 A112780

Keyword

nonn,easy

Author

Ray Chandler, Nov 10 2005

Status

approved