A050797 Numbers n such that n^2 - 1 is expressible as the sum of two nonzero squares in exactly one way.

3, 9, 17, 19, 33, 35, 73, 145, 161, 163, 195, 243, 393, 483, 513, 721, 723, 1153, 1763, 2177, 2305, 2593, 4803, 5185, 5833, 6273, 6963, 7057, 7395, 8713, 9523, 9603, 10083, 12483, 13923, 14113, 15875, 17425, 17673, 19043, 20737

Offset: 1

Author

Patrick De Geest, Sep 15 1999

Keywords

• nonn
• nice

Comments

If the definition were changed from "nonzero squares" to "nonnegative squares", there would be just one additional term, 1. - T. D. Noe, May 27 2008

Examples

			E.g. 393^2 - 1 = 28^2 + 392^2 only.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..300
• Eric Weisstein, MathWorld: Sum of Squares Function
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A050798, A050795.

Cf. A000161

Programs

Mathematica

twoSquaresQ[ n_] := (r = Reduce [0 < a <= b && n^2 - 1 == a^2 + b^2, {a, b}, Integers]; Head[r] === And); Select[ Range[21000], twoSquaresQ] (* Jean-François Alcover, Oct 10 2011 *)

Extensions

More terms from James Sellers