A240937 Least number k >= 0 such that n! + k is a cube.

0, 6, 2, 3, 5, 9, 792, 2555, 10368, 23464, 84888, 1047087, 2483200, 54721675, 228537856, 1394007616, 5090444477, 51286309703, 608427634303, 3260058995493, 11314112766137, 51848285189219, 1034026438223449, 11075640379838488, 181108172062981288, 1566869630866485093

Offset: 1

Author

Derek Orr, Aug 03 2014

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..524

Crossrefs

Cf. A068869.

Programs

Maple

f:= proc(n) local N; N:= n!; ceil(N^(1/3))^3 - N end proc:
seq(f(n), n=1..30); # Robert Israel, Aug 04 2014

Mathematica

f[n_] := Block[{c = n! - 1}, (1 + Floor[c^(1/3)])^3 - c - 1]; Array[f, 26] (* Robert G. Wilson v, Aug 04 2014 *)
Table[Ceiling[CubeRoot[n!]]^3-n!,{n,30}] (* Harvey P. Dale, Jun 21 2025 *)

PARI

a(n)=for(k=0,10^10,s=n!+k;if((ispower(s)&&ispower(s)%3==0)||s==1,return(k)))
n=1;while(n<20,print1(a(n),", ");n++)

PARI

vector(50, n, ceil(n!^(1/3))^3-n!) \\ faster program

Extensions

a(15) onward from Robert G. Wilson v, Aug 04 2014