login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A145355 a(n) = round(round(sqrt(n!)/abs(round(sqrt(n!))^2 - n!))). 1
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 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A100298 A066461 A117069 * A110353 A097720 A077806

Adjacent sequences:  A145352 A145353 A145354 * A145356 A145357 A145358

KEYWORD

nonn

AUTHOR

Alexander R. Povolotsky, Oct 09 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 21 06:14 EST 2021. Contains 340333 sequences. (Running on oeis4.)