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A000099 Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.
(Formerly M1374 N0534)
6

%I M1374 N0534

%S 1,2,5,10,20,24,26,41,53,130,149,205,234,287,340,410,425,480,586,840,

%T 850,986,1680,1843,2260,2591,3023,3024,3400,3959,3960,5182,5183,7920,

%U 9796,11233,14883,15119,15120,19593,21600,21603,21604,22177,28559,28560

%N Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David W. Wilson, <a href="/A000099/b000099.txt">Table of n, a(n) for n = 1..200</a>

%H W. C. Mitchell, <a href="http://dx.doi.org/10.1090/S0025-5718-1966-0195834-3">The number of lattice points in a k-dimensional hypersphere</a>, Math. Comp., 20 (1966), 300-310.

%t nmax = 3*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; A000099 = Reap[For[k = 0; n = 1, n <= nmax, n++, p = Abs[P[n]]; If[p > record, record = p; k++; Sow[n]; Print["a(", k, ") = ", n];]]][[2, 1]] (* _Jean-Fran├žois Alcover_, Feb 03 2016 *)

%Y Cf. A000323, A000036, A000092, A000413, A000223.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Entry revised by _N. J. A. Sloane_, Jun 26 2005

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Last modified November 16 20:06 EST 2019. Contains 329204 sequences. (Running on oeis4.)