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A068527
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Difference between smallest square >= n and n.
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25
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0, 0, 2, 1, 0, 4, 3, 2, 1, 0, 6, 5, 4, 3, 2, 1, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9
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OFFSET
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0,3
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COMMENTS
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The greedy inverse (sequence of the smallest k such that a(k)=n) starts 0, 3, 2, 6, 5, 11, 10, 18, 17, 27, 26, 38, 37, 51, 50, ... and appears to be given by A010000 and A002522, interleaved. - R. J. Mathar, Nov 17 2014
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LINKS
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Ivan Panchenko, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = A048761(n) - n = ceiling(sqrt(n))^2 - n.
G.f.: (-x^2 + (x-x^2)*Sum_{m>=1} (1+2*m)*x^(m^2))/(1-x)^2. This sum is related to Jacobi Theta functions. - Robert Israel, Nov 17 2014
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MAPLE
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A068527:=n->ceil(sqrt(n))^2-n; seq(A068527(n), n=0..100); # Wesley Ivan Hurt, Jun 11 2014
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MATHEMATICA
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Table[Ceiling[Sqrt[n]]^2-n, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)
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PROG
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(MAGMA) [ Ceiling(Sqrt(n))^2-n : n in [0..50] ]; // Wesley Ivan Hurt, Jun 11 2014
(PARI) a(n)=if(issquare(n), 0, (sqrtint(n)+1)^2-n) \\ Charles R Greathouse IV, Oct 22 2014
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CROSSREFS
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Cf. A053186, A068869, A066857.
Sequence in context: A334122 A086802 A092488 * A218599 A051623 A244124
Adjacent sequences: A068524 A068525 A068526 * A068528 A068529 A068530
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KEYWORD
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nonn,easy
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AUTHOR
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Vladeta Jovovic, Mar 21 2002
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STATUS
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approved
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