OFFSET
2,3
COMMENTS
This sequence suggests that the distance between a factorial and the closest power is tightly bounded. Generated by Ed Pegg Jr in response to three Alexander R. Povolotsky conjectures: 1)n! + n^2 != m^2 (except for trivial case with n=0, m=1) per conducted calculations doesn't yield any solutions from n=1 to n= 200,000 2)n! + Sum(j^2, j=1, j=n) != m^2 per conducted calculations doesn't yield any solutions from n=1 to n= 2,000,000 3)n! + prime(n) != m^k is too difficult to cover by exhaustive calculations ...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 2..10000
PROG
(PARI) a(n)=my(s=round(sqrt(n!))); s\/abs(s^2-n!) \\ Charles R Greathouse IV, Dec 20 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander R. Povolotsky, Oct 09 2008
STATUS
approved