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a(n) = 1 if x^2 + 1 = n * y^2 has infinitely many solutions in integers (x,y), otherwise a(n) = 0.
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%I #15 Aug 29 2020 10:47:09

%S 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,

%T 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,

%U 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

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

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

%H John Robertson, <a href="https://web.archive.org/web/20051102095831/http://hometown.aol.com/jpr2718/pell.pdf">Solving the generalized Pell equation x^2-dy^2=N</a>.

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

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

%Y Cf. A068717, A067280, A006702, A006703.

%K nonn

%O 1,1

%A _Frank Ellermann_, Feb 25 2002

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