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 A049240 Smallest nonnegative value taken on by x^2 - n*y^2 for an infinite number of integer pairs (x, y). 13
 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Encodes to 1,2,1,4,1,6,1,8,1,10,...: unsigned version of A009531. - Paul Barry, Oct 12 2005 Parity of inverse Moebius transform of Jacobsthal numbers J(k) less J(n). - Paul Barry, Oct 12 2005 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 Index entries for characteristic functions Index entries for sequences computed from exponents in factorization of n FORMULA a(n) = 0 if n is square, 1 otherwise. a(n) = (A001045(n) - Sum_{k|n} A001045(k)) mod 2. - Paul Barry, Oct 12 2005 a(n) = 1 - A010052(n). - R. J. Mathar, Jul 04 2009 a(n) = floor(1+ceiling(sqrt(n))-floor(sqrt((n)))/2). - Wesley Ivan Hurt, Sep 27 2014 G.f.: (1+x)/(2-2*x) - (1/2)*theta_3(0,x) where theta_3 is a Jacobi theta function. - Robert Israel, Oct 02 2014 MAPLE A049240:=n->`if`(issqr(n), 0, 1): seq(A049240(n), n=1..100); # Wesley Ivan Hurt, Sep 27 2014 MATHEMATICA Differences[Table[n - Ceiling[Sqrt[n]], {n, 105}]] (* Arkadiusz Wesolowski, Oct 30 2012 *) Table[Floor[(1 + Ceiling[Sqrt[n]] - Floor[Sqrt[n]])/2], {n, 70}] (* Wesley Ivan Hurt, Sep 27 2014 *) PROG (Magma) [Floor((1 + Ceiling(Sqrt(n)) - Floor(Sqrt(n)))/2) : n in [1..100]]; // Wesley Ivan Hurt, Sep 27 2014 (Python) from math import isqrt def A049240(n): return int(isqrt(n)**2!=n) # Chai Wah Wu, Jun 14 2022 CROSSREFS Cf. A001045, A005931, A010052. Characteristic function of A000037 (the nonsquares). Sequence in context: A285418 A344617 A068717 * A285978 A138712 A029693 Adjacent sequences: A049237 A049238 A049239 * A049241 A049242 A049243 KEYWORD nonn,easy AUTHOR David W. Wilson STATUS approved

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Last modified July 17 05:50 EDT 2024. Contains 374360 sequences. (Running on oeis4.)