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

Author

Jonathan Vos Post, May 03 2005

Keywords

• easy
• nonn

Links

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

Crossrefs

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

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

Programs

Magma

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

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 *)

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

Extensions

Extended by Ray Chandler, May 03 2005