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A000323 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)).
(Formerly M3787 N1543)
6
5, 9, 21, 37, 69, 69, 89, 137, 177, 421, 481, 657, 749, 885, 1085, 1305, 1353, 1489, 1861, 2617, 2693, 3125, 5249, 5761, 7129, 8109, 9465, 9465, 10717, 12401, 12401, 16237, 16237, 24833, 30725, 35237, 46701, 47441, 47441, 61493, 67797, 67805, 67805 (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
W. C. Mitchell, The number of lattice points in a k-dimensional hypersphere, Math. Comp., 20 (1966), 300-310.
MATHEMATICA
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*)
CROSSREFS
Sequence in context: A147018 A081883 A049744 * A146131 A083943 A097074
KEYWORD
nonn
AUTHOR
EXTENSIONS
Entry revised Jun 28 2005
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)