A106483 - OEIS

%I #41 Sep 17 2024 15:44:31

%S 2,3,7,11,13,17,41,43,59,73,109,113,127,137,157,179,181,197,199,211,

%T 251,263,277,293,311,353,367,379,409,419,433,487,563,571,577,617,619,

%U 659,701,739,743,757,797,811,827,829,839,857,937,941,1009,1039,1063

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

%H Alois P. Heinz, <a href="/A106483/b106483.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

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

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

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

%F a(n) = prime(A092058(n)). - _R. J. Mathar_, Aug 20 2019

%p q:= p-> andmap(isprime, [p, 2*p^2-1]):

%p select(q, [$2..2000])[];  # _Alois P. Heinz_, Jun 21 2022

%t Select[Table[Prime[n], {n, 500}], PrimeQ[2*#^2 - 1] &] (* _Ray Chandler_, May 03 2005 *)

%o (Magma) [p: p in PrimesUpTo(2500)|  IsPrime(2*p^2-1)]; // _Vincenzo Librandi_, Jan 29 2011

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

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

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, May 03 2005

%E Extended by _Ray Chandler_, May 03 2005