A070929 Smallest integer >= 0 of the form x^2 - n^3.

0, 0, 1, 9, 0, 19, 9, 18, 17, 0, 24, 38, 36, 12, 65, 106, 0, 128, 97, 30, 100, 148, 168, 154, 100, 0, 113, 198, 249, 260, 225, 138, 356, 163, 297, 389, 0, 423, 353, 217, 9, 248, 441, 17, 80, 79, 8, 506, 297, 0, 316, 574, 17, 119, 145, 89, 784, 568, 252, 737, 225, 548

Offset

0,4

Comments

a(n)=0 iff n is a square.

Links

Table of n, a(n) for n=0..61.

Formula

a(n) = ceiling(n^(3/2))^2 - n^3 = A077115(n) - n^3.

Example

A077115(10) = 1024 = 32^2 is the least square >= 10^3 = 1000, therefore a(10) = 1024 - 1000 = 24.

Mathematica

f[n_]=Ceiling[n^(3/2)]^2-n^3;
t1=Table[f[n], {n, 1, 90}]; t1 (* Clark Kimberling, Jan 30 2011 *)

Prog

(PARI) for(n=1, 100, print1(ceil(n^(3/2))^2-n^3, ", "))

Crossrefs

Cf. A000578, A077116, A077118, A077119, A070923, A068527.

Sequence in context: A117465 A136679 A299154 * A007394 A067153 A057405

Adjacent sequences: A070926 A070927 A070928 * A070930 A070931 A070932

Keyword

easy,nonn

Author

Benoit Cloitre, May 20 2002

Status

approved