A174165 Numbers n for which (prime(n) - 1)^2 +1 is prime.

1, 2, 3, 4, 5, 7, 12, 13, 19, 31, 32, 36, 37, 42, 47, 53, 54, 55, 58, 60, 63, 78, 79, 82, 83, 91, 94, 102, 105, 106, 118, 125, 126, 133, 135, 144, 155, 156, 159, 161, 163, 178, 184, 190, 206, 210, 214, 216, 219, 247, 248, 284, 286, 288, 307, 313, 315, 322

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 10 2010

Keywords

• nonn

Examples

			a(1) = 1 because (1st prime -1)^2 +1 = (2-1)^2 +1 = 2, a prime; a(2) = 2 because (2nd prime -1)^2 +1 = (3-1)^2 +1 = 5, a prime; a(3) = 3 because (3rd prime -1)^2 +1 = (5-1)^2 +1 = 17, a prime; ... ; a(6) # 6 since (6th prime -1)^2 = (13-1)^2 +1 = 145 = 5*29, which is not a prime; etc.
		

Crossrefs

Cf. A000040, A006093, A005722 & A127435.

Programs

Mathematica

fQ[n_] := PrimeQ[ (Prime@n - 1)^2 + 1]; Select[ Range@ 335, fQ@# &]

Extensions

Edited, corrected and extended by Robert G. Wilson v, Mar 14 2010