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)).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign

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.

Crossrefs

Cf. A000092, A000099, A000223, A000323, A000413.

Programs

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 *)

Formula

a(n) = round(P(A000099(n))), where P(n) = A057655(n)-pi*n. - David W. Wilson, May 15 2008

Extensions

Revised by N. J. A. Sloane, Jun 26 2005

More terms from David W. Wilson, May 15 2008