A158526 n and (1 + 2*n + 2*n^2) are primes.

2, 5, 7, 17, 19, 29, 47, 79, 97, 109, 137, 139, 149, 157, 167, 199, 229, 347, 349, 389, 409, 467, 479, 547, 577, 599, 709, 719, 757, 857, 929, 937, 967, 1039, 1069, 1087, 1187, 1229, 1259, 1399, 1409, 1447, 1559, 1579, 1597, 1607, 1657, 1697, 1699, 1709

Offset

1,1

Comments

Numbers n such that A048395(n) is semiprime, or A048395(n)/n is prime.

Or, primes in A027861. Also, (1+2*n+2*n^2) are in A027862. - Zak Seidov, Sep 19 2015

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

A048395(2)=26=2*13, A048395(5)=305=5*61, A048395(7)=791=7*113.

Mathematica

f[n_]:=PrimeQ[n^2+(n+1)^2]; lst={}; Do[p=Prime[n]; If[f[p], AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *)

Prog

(PARI) forprime(p=2, 1e4, if(isprime(2*p*(p+1)+1), print1(p", "))) \\ Charles R Greathouse IV, Sep 09 2009
(Magma) [p: p in PrimesUpTo(2000) | IsPrime(2*p^2+2*p+1)]; // Vincenzo Librandi, Jun 22 2014

Crossrefs

Cf. A048395 (sum of consecutive nonsquares), A001358 (semiprimes).

Cf. A027861, A027862.

Sequence in context: A038875 A019334 A045356 * A146364 A105895 A238699

Adjacent sequences: A158523 A158524 A158525 * A158527 A158528 A158529

Keyword

nonn,easy

Author

Zak Seidov, Mar 20 2009

Status

approved