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 A000036 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) 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES 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). LINKS 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. FORMULA a(n) = round(P(A000099(n))), where P(n) = A057655(n)-pi*n. - David W. Wilson, May 15 2008 MATHEMATICA 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 *) CROSSREFS Cf. A000092, A000099, A000223, A000323, A000413. Sequence in context: A247548 A001600 A175578 * A165081 A165089 A165083 Adjacent sequences:  A000033 A000034 A000035 * A000037 A000038 A000039 KEYWORD sign AUTHOR EXTENSIONS Revised by N. J. A. Sloane, Jun 26 2005 More terms from David W. Wilson, May 15 2008 STATUS approved

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