A052291 Primes p such that 4p^2 + 1 is also prime.

2, 3, 5, 7, 13, 37, 47, 67, 73, 103, 157, 163, 193, 233, 317, 337, 547, 587, 647, 653, 677, 683, 773, 827, 883, 887, 947, 983, 1013, 1063, 1087, 1163, 1297, 1327, 1373, 1487, 1493, 1523, 1553, 1567, 1607, 1627, 1637, 1657, 1663, 1667, 1723, 1867, 1873

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Marek Wolf, Search for primes of the form m^2+1, arXiv:0803.1456 [math.NT], 2008-2010.

Example

The 5th term is 13 and 4*169+1 = 677 is also a prime.

Mathematica

Select[Prime[Range[300]], PrimeQ[4 #^2 + 1]&] (* Vincenzo Librandi, Apr 11 2013 *)

Prog

(Magma) [p: p in PrimesUpTo(2000) | IsPrime(4*p^2+1)]; // Vincenzo Librandi, Apr 11 2013

Crossrefs

Cf. A052292.

Sequence in context: A140768 A192578 A050779 * A256072 A072826 A084761

Adjacent sequences: A052288 A052289 A052290 * A052292 A052293 A052294

Keyword

nonn,easy

Author

Labos Elemer, Feb 08 2000

Status

approved