A145355 a(n) = round(round(sqrt(n!)/abs(round(sqrt(n!))^2 - n!))).

1, 1, 5, 11, 3, 71, 2, 1, 8, 20, 5, 1, 2, 5, 1, 2, 2, 1, 1, 3, 1, 1, 8, 2, 13, 22, 1, 1, 3, 2, 2, 3, 2, 2, 1, 2, 3, 2, 3, 1, 9, 2, 2, 1, 2, 1, 1, 2, 2, 1, 6, 1, 1, 4, 2, 2, 2, 3, 21, 2, 1, 1, 1, 1, 2, 2, 6, 8, 4, 7, 1, 2, 2, 1, 3, 1, 1, 9, 2, 1, 2, 4, 3, 5, 1, 1, 2, 5, 13, 6

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=2*10^5.

2) n! + Sum_{j=1..n} j^2 != m^2 per conducted calculations doesn't yield any solutions from n=1 to n=2*10^6.

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

Sequence in context: A066461 A351654 A117069 * A351338 A110353 A377050

Adjacent sequences: A145352 A145353 A145354 * A145356 A145357 A145358

Keyword

nonn

Author

Alexander R. Povolotsky, Oct 09 2008

Status

approved