A109685 Smallest nontrivial perfect power with same leading digits as n!.

16, 25, 64, 243, 120409, 720801, 5040025, 4032064, 362880940816, 3628800213481, 3991680051905536, 47900160082546704, 6227020800662405184, 8717829120075164064361, 1307674368000199069586496, 2092278988800044062720986249, 355687428096000138859491069121

Offset

1,1

Links

Table of n, a(n) for n=1..17.

Prog

(PARI) for(n=1, 22, pp=0; lmin=n!; lmax=lmin; while(!pp, lexp=floor(log(lmax)/log(2)); for(e=2, lexp, cmin=ceil((lmin)^(1/e)); if(cmin<=floor((lmax)^(1/e)), if(pp, pp=min(cmin^e, pp), pp=cmin^e))); lmin*=10; lmax=lmax*10+9); print1(pp", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 22 2007

Crossrefs

Sequence in context: A110922 A065408 A112392 * A188826 A152152 A260047

Adjacent sequences: A109682 A109683 A109684 * A109686 A109687 A109688

Keyword

base,nonn

Author

Jason Earls, Aug 07 2005

Extensions

More terms from Ryan Propper, Jun 13 2006

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 22 2007

Status

approved