A068716 a(n) = 1 if x^2 + 1 = n * y^2 has infinitely many solutions in integers (x,y), otherwise a(n) = 0.

0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0

Offset: 1

Author

Frank Ellermann, Feb 25 2002

Keywords

• nonn

Examples

			a(2) = 1 as x*x + 1 = 2 * y*y is soluble, e.g., 7*7 + 1= 2*5*5.
		

References

• H. Davenport, The Higher Arithmetic. Cambridge Univ. Press, 7th ed., 1999, table 1.

Links

• John Robertson, Solving the generalized Pell equation x^2-dy^2=N.

Crossrefs

Cf. A068717, A067280, A006702, A006703.

Formula

a(n) = 1 - (A067280(n) mod 2 ).

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 31 2003