A002938 The minimal sequence from solving n^3 - m^2 = a(n). (Formerly M0033 N0008)

0, 1, 2, 0, 4, 9, 18, 17, 0, 24, 35, 36, 12, 40, 11, 0, 13, 56, 30, 79, 45, 39, 67, 100, 0, 113, 83, 48, 53, 104, 138, 7, 163, 100, 26, 0, 28, 116, 217, 9, 248, 104, 17, 80, 79, 8, 139, 297, 0, 316, 155, 17, 119, 145, 89, 55, 293, 252, 170, 225, 405, 184, 47, 0, 49

Offset

1,3

References

Marshall Hall, Jr., The Diophantine equation x^3-y^2=k, pp. 173-198 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

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

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = |A077119(n+1)|.

a(n^2) = 0. - Benoit Cloitre, Aug 17 2002

Mathematica

f1[n_] := n - Floor[Sqrt[n]]^2;
f2[n_] := Ceiling[Sqrt[n]]^2-n;
Table[Min[f1[n^3], f2[n^3]], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2010 *)

Prog

(PARI) a(n)=vecmin(vector(ceil(n^(3/2)), i, abs(n^3-i^2)))

Crossrefs

Cf. A077119.

Sequence in context: A287314 A358564 A077119 * A111938 A224822 A246928

Adjacent sequences: A002935 A002936 A002937 * A002939 A002940 A002941

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Benoit Cloitre, Aug 17 2002

Status

approved