A049002 Primes of form p^2 - 2, where p is prime.

2, 7, 23, 47, 167, 359, 839, 1367, 1847, 2207, 3719, 5039, 7919, 10607, 11447, 16127, 17159, 19319, 29927, 36479, 44519, 49727, 54287, 57119, 66047, 85847, 97967, 113567, 128879, 177239, 196247, 201599, 218087, 241079, 273527, 292679, 323759

Offset: 1

Author

Herman H. Rosenfeld (herm3(AT)pacbell.net)

Keywords

• nonn
• easy

Examples

			127^2 - 2 = 16127.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Primes in A049001.

Cf. A062326 (values of p).

Cf. A010051.

Programs

Haskell

a049002 n = a049002_list !! (n-1)
a049002_list = filter ((== 1) . a010051') a049001_list
-- Reinhard Zumkeller, Jul 30 2015

Magma

[a: p in PrimesUpTo(1000) | IsPrime(a) where a is p^2-2 ]; // Vincenzo Librandi, Apr 29 2015

Mathematica

f[n_]:=n^2-2; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,f[p]]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 16 2009 *)
Select[Prime[Range[150]]^2 - 2, PrimeQ] (* Vincenzo Librandi, Apr 29 2015 *)

PARI

lista(nn) = forprime(p=1, nn, if (isprime(q=p^2-2), print1(q, ", "))); \\ Michel Marcus, Jan 08 2015

Sage

a = lambda p: p^2-2
[a(p) for p in primes(600) if is_prime(a(p))] # Bruno Berselli, Apr 29 2015

Formula

a(n) = A062326(n)^2-2. - Zak Seidov, Apr 29 2015

Extensions

More terms from James Sellers