cp's OEIS Frontend

A000092 Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.

%I A000092 M1326 N0508 #32 Dec 19 2022 10:17:30
%S A000092 1,2,5,6,14,21,29,30,54,90,134,155,174,230,234,251,270,342,374,461,
%T A000092 494,550,666,750,810,990,1890,2070,2486,2757,2966,3150,3566,3630,4554,
%U A000092 4829,5670,5750,8154,8382,8774,8910,10350,10710,15734,15750,16302,17550
%N A000092 Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.
%C A000092 Indices n for which A210641(n) = A117609(n) - A210639(n) yields record values (in absolute value). - _M. F. Hasler_, Mar 26 2012
%D A000092 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000092 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000092 Seth A. Troisi, <a href="/A000092/b000092.txt">Table of n, a(n) for n = 1..131</a>
%H A000092 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.
%H A000092 Seth A. Troisi, <a href="https://github.com/sethtroisi/OEIS/tree/main/A000092">Python program</a>
%t A000092 P[n_] := Sum[SquaresR[3, k], {k, 0, n}] - Round[(4/3)*Pi*n^(3/2)]; record = 0; A000092 = Reap[For[n=1, n <= 2*10^4, n++, If[(p = Abs[P[n]]) > record, record = p; Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Feb 04 2016, after _M. F. Hasler_ *)
%o A000092 (PARI) m=0; for(n=1,1e4, if(m+0<m=max(abs(A210641(n)),m),print1(n",")))  /* Start with n=0 to print the initial 0. */ \\ _M. F. Hasler_, Mar 26 2012
%Y A000092 Cf. A000323, A000036, A000099, A000413, A000223.
%K A000092 nonn
%O A000092 1,2
%A A000092 _N. J. A. Sloane_
%E A000092 Revised Jun 28 2005