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A000036
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Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); A000099 gives values of n where |P(n)| sets a new record; sequence gives closest integer to P(A000099(n)).
(Formerly M0610 N0221)
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7
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2, 3, 5, 6, 6, -6, 7, 8, 10, 13, 13, 13, 14, -17, 17, 17, 18, -19, 20, -22, 23, 27, -29, -29, 29, -31, -32, -35, 36, -37, -40, -43, -46, -48, -50, -53, -55, -57, -60, -60, -61, -63, -66, -66, -68, -71, -74, -77, -79, -82, -85, -88, -89, -92, -95, -96, -97, -97, -100
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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David W. Wilson, Table of n, a(n) for n = 1..200
W. C. Mitchell, The number of lattice points in a k-dimensional hypersphere, Math. Comp., 20 (1966), 300-310.
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FORMULA
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a(n) = round(P(A000099(n))), where P(n) = A057655(n)-pi*n. - David W. Wilson, May 15 2008
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MATHEMATICA
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nmax = 6*10^4; A[n_] := 1 + 4*Floor[Sqrt[n]] + 4*Floor[Sqrt[n/2]]^2 + 8* Sum[Floor[Sqrt[n - j^2]], {j, Floor[Sqrt[n/2]] + 1, Floor[Sqrt[n]]}]; V[n_] := Pi*n; P[n_] := A[n] - V[n]; record = 0; A000036 = Reap[For[k = 0; n = 1, n <= nmax, n++, p = Abs[pn = P[n]]; If[p > record, record = p; k++; Sow[pn // Round]; Print["a(", k, ") = ", pn // Round]]]][[2, 1]] (* Jean-François Alcover, Feb 03 2016 *)
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CROSSREFS
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Cf. A000092, A000099, A000223, A000323, A000413.
Sequence in context: A347861 A316609 A307327 * A165081 A165089 A165083
Adjacent sequences: A000033 A000034 A000035 * A000037 A000038 A000039
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Revised by N. J. A. Sloane, Jun 26 2005
More terms from David W. Wilson, May 15 2008
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STATUS
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approved
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