A137291 Numbers m such that prime(m)^2-2 is prime.

1, 2, 3, 4, 6, 8, 10, 12, 14, 15, 18, 20, 24, 27, 28, 31, 32, 34, 40, 43, 47, 48, 51, 52, 55, 62, 65, 68, 72, 82, 86, 87, 91, 94, 99, 100, 104, 107, 111, 119, 123, 128, 129, 130, 132, 133, 134, 135, 139, 141, 150, 152, 170, 172, 177, 180, 182, 191, 200, 202, 209, 211

Offset: 1

Author

Ctibor O. Zizka, Apr 05 2008

Keywords

• easy
• nonn

Comments

For m>=1, for these and only these numbers m, A242719(m) = prime(m)^2 + 1. Since A242719(m) >= prime(m)^2 + 1, then the equality is obtained on this and only this sequence. - Vladimir Shevelev, Sep 04 2014

Examples

			prime(24)*prime(24)-2 = 89*89-2 = 7919 is prime, so n=24 belongs to the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A062326, A242719, A242720, A246824, A010051, A049001, A103960, A210481.

Programs

Haskell

a137291 n = a137291_list !! (n-1)
a137291_list = filter ((== 1) . a010051' . a049001) [1..]
-- Reinhard Zumkeller, Jul 30 2015

Mathematica

Select[Range[211],PrimeQ[Prime[#]^2-2]&] (* James C. McMahon, May 28 2025 *)

PARI

is(n,p=prime(n))=isprime(p^2-2) \\ Charles R Greathouse IV, Feb 17 2017

Formula

A103960(a(n)) - A210481(a(n)) = 1. - Reinhard Zumkeller, Jul 30 2015

a(n) = A049084(A049002(n)). - R. J. Mathar, Apr 09 2008

Extensions

More terms from R. J. Mathar, Apr 09 2008

Offset corrected by Reinhard Zumkeller, Jul 30 2015