A225078 Numbers n such that n^2+1 and (n+1)^2-2 are both prime.

1, 2, 4, 6, 14, 20, 26, 36, 54, 74, 116, 120, 126, 130, 134, 160, 176, 204, 210, 230, 236, 256, 264, 284, 300, 314, 340, 386, 420, 440, 466, 490, 496, 544, 594, 636, 644, 714, 750, 760, 784, 816, 930, 950, 986, 1070, 1124, 1140, 1146, 1156, 1174, 1176, 1210

Offset: 1

Author

César Aguilera, Apr 26 2013

Keywords

• nonn

Comments

Prime limits of the Legendré conjecture for a given n.

Examples

			n=2; n+1=3 ;n^2+1=5 and (n+1)^2-2=7.
n=490; n+1=491; n^2+1=240101 and (n+1)^2-2=241079.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Legendre's Conjecture
• Wikipedia, Legendre's conjecture

Crossrefs

Cf. A002522, A008865, A010051, A014085, A002496, A028871.

Programs

Haskell

import Data.Function (on)
import Data.List (elemIndices)
a225078 n = a225078_list !! (n-1)
a225078_list = elemIndices 1 $
   zipWith ((*) `on` a010051') a002522_list a008865_list
-- Reinhard Zumkeller, May 06 2013

Mathematica

Select[Range[2000], PrimeQ[#^2 + 1] && PrimeQ[(# + 1)^2 - 2] &] (* T. D. Noe, May 06 2013 *)