A106483 Primes p such that 2*p^2 - 1 is also prime.

2, 3, 7, 11, 13, 17, 41, 43, 59, 73, 109, 113, 127, 137, 157, 179, 181, 197, 199, 211, 251, 263, 277, 293, 311, 353, 367, 379, 409, 419, 433, 487, 563, 571, 577, 617, 619, 659, 701, 739, 743, 757, 797, 811, 827, 829, 839, 857, 937, 941, 1009, 1039, 1063

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Formula

a(n) is in this sequence iff A007588(a(n)) is an element of A001358.

a(n) is in this sequence iff A106482(a(n)) = 2.

a(n) is in this sequence iff a(n) is prime and 2*a(n)^2-1 is also prime.

a(n) = prime(A092058(n)). - R. J. Mathar, Aug 20 2019

Maple

q:= p-> andmap(isprime, [p, 2*p^2-1]):
select(q, [$2..2000])[];  # Alois P. Heinz, Jun 21 2022

Mathematica

Select[Table[Prime[n], {n, 500}], PrimeQ[2*#^2 - 1] &] (* Ray Chandler, May 03 2005 *)

Prog

(Magma) [p: p in PrimesUpTo(2500)|  IsPrime(2*p^2-1)]; // Vincenzo Librandi, Jan 29 2011

Crossrefs

Cf. A000040, A001358, A007588, A106482, A106484, A177104 (2p^3-1 prime), A182785 (2p^4-1 prime)

Cf. A092057 (2p^2 - 1).

Sequence in context: A023221 A127430 A171595 * A145673 A321657 A040116

Adjacent sequences: A106480 A106481 A106482 * A106484 A106485 A106486

Keyword

easy,nonn

Author

Jonathan Vos Post, May 03 2005

Extensions

Extended by Ray Chandler, May 03 2005

Status

approved