A130177 For p = the n-th prime, a(n) = the least prime q greater than p+2 such that (p^2+q^2)/2 - 1 is a square, or a(n) = 0 if there is no such prime.

0, 11, 263, 59, 23, 101, 109, 1278886952463697, 151, 193, 79, 269, 277, 311, 0, 179, 83, 83003, 479, 487, 181, 563, 571, 613, 1201, 157, 141509, 739, 773, 479, 6858037981, 907, 1291, 983, 227, 6133, 1109, 1151, 54331, 1201, 431, 307, 1327

Offset: 1

Author

Nick Hobson, May 14 2007

Keywords

• nonn

Examples

			a(3) = 263 because (5^2+263^2)/2-1 = 186^2.
a(4) = 59 because (7^2+59^2)/2-1 = 42^2.
a(5) = 23 because (11^2+23^2)/2-1 = 18^2.
		

Links

• Don Reble, Table of n, a(n) for n=1..787
• Dean Hickerson, Proof that a(15) = 0
• Number Theory Web, Solving x^2-Dy^2=N
• J. P. Robertson, Solving the Generalized Pell Equation

Extensions

Edited by T. D. Noe and Don Reble, May 14 2007