A068716 - OEIS

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

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OFFSET

1,1

REFERENCES

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

LINKS

Table of n, a(n) for n=1..105.

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

FORMULA

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

EXAMPLE

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