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%I M3787 N1543 #22 Feb 01 2022 00:53:22
%S 5,9,21,37,69,69,89,137,177,421,481,657,749,885,1085,1305,1353,1489,
%T 1861,2617,2693,3125,5249,5761,7129,8109,9465,9465,10717,12401,12401,
%U 16237,16237,24833,30725,35237,46701,47441,47441,61493,67797,67805,67805
%N 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 A(A000099(n)).
%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="/A000323/b000323.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[an = A[n]]; Print["a(", k, ") = ", an];]]][[2, 1]] (* _Jean-François Alcover_, Feb 07 2016*)
%Y Cf. A000099, A000036, A000092, A000413, A000223.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Entry revised Jun 28 2005
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