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

1,1

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

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

Example

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

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 *)

Crossrefs

Cf. A050798, A050795.

Cf. A000161

Sequence in context: A174180 A106676 A050795 * A103967 A032400 A329422

Adjacent sequences: A050794 A050795 A050796 * A050798 A050799 A050800

Keyword

nonn,nice

Author

Patrick De Geest, Sep 15 1999

Extensions

More terms from James A. Sellers

Status

approved