cp's OEIS Frontend

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.

%I A000099 M1374 N0534 #29 Feb 03 2016 16:02:54
%S A000099 1,2,5,10,20,24,26,41,53,130,149,205,234,287,340,410,425,480,586,840,
%T A000099 850,986,1680,1843,2260,2591,3023,3024,3400,3959,3960,5182,5183,7920,
%U A000099 9796,11233,14883,15119,15120,19593,21600,21603,21604,22177,28559,28560
%N 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.
%D A000099 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000099 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000099 David W. Wilson, <a href="/A000099/b000099.txt">Table of n, a(n) for n = 1..200</a>
%H A000099 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 A000099 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-François Alcover_, Feb 03 2016 *)
%Y A000099 Cf. A000323, A000036, A000092, A000413, A000223.
%K A000099 nonn
%O A000099 1,2
%A A000099 _N. J. A. Sloane_
%E A000099 Entry revised by _N. J. A. Sloane_, Jun 26 2005