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 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

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