A240940 Least number k >= 0 such that n! - k is a perfect power.

0, 1, 2, 8, 20, 44, 127, 320, 476, 3584, 12311, 4604, 74879, 414119, 2071775, 5703551, 11551671, 45680444, 442548224, 1960632176, 2657058876, 24923993276, 130518272975, 1478154932316, 5446454455004, 38610655379975, 204033398880671, 538347188396016, 3809155729331900, 27460809907547975, 52607402757814775

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Prog

(PARI)
a(n)=for(k=0, n!, s=n!-k; if(ispower(s)||s==1, return(k)))
n=1; while(n<50, print1(a(n), ", "); n++)
(PARI)
a(n)=for(k=1, n!, if(2^k>n!, kk=k; break)); if(kk==1, return(0)); L=List([]); for(i=2, kk, listinsert(L, n!-floor(n!^(1/i))^i, 1)); listsort(L); L[1]
vector(40, n, a(n)) \\ faster program

Crossrefs

Cf. A066857 (n! - k is a square), A226973.

Sequence in context: A131128 A296954 A203604 * A066857 A146168 A058405

Adjacent sequences: A240937 A240938 A240939 * A240941 A240942 A240943

Keyword

nonn

Author

Derek Orr, Aug 04 2014

Status

approved