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. (Formerly M1326 N0508)

1, 2, 5, 6, 14, 21, 29, 30, 54, 90, 134, 155, 174, 230, 234, 251, 270, 342, 374, 461, 494, 550, 666, 750, 810, 990, 1890, 2070, 2486, 2757, 2966, 3150, 3566, 3630, 4554, 4829, 5670, 5750, 8154, 8382, 8774, 8910, 10350, 10710, 15734, 15750, 16302, 17550

Offset

1,2

Comments

Indices n for which A210641(n) = A117609(n) - A210639(n) yields record values (in absolute value). - M. F. Hasler, Mar 26 2012

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

Seth A. Troisi, Table of n, a(n) for n = 1..131

W. C. Mitchell, The number of lattice points in a k-dimensional hypersphere, Math. Comp., 20 (1966), 300-310.

Seth A. Troisi, Python program

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000323, A000036, A000099, A000413, A000223.

Sequence in context: A245540 A211369 A006596 * A100630 A275839 A057302

Adjacent sequences: A000089 A000090 A000091 * A000093 A000094 A000095

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Revised Jun 28 2005

Status

approved