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 A082995 Distance from n!+1 to next larger square. 1
 2, 1, 2, 0, 0, 8, 0, 80, 728, 224, 323, 39168, 82943, 176399, 215295, 3444735, 26167683, 114349224, 255004928, 1158920360, 11638526760, 42128246888, 191052974115, 97216010328, 2430400258224, 1553580508515, 4666092737475 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The only known values of n such that n!+1 is a perfect square are 4, 5 and 7. Paul Leyland, et al. have found no other solutions for n <= 1 million (see link). For 1 <= n <= 11, n!+1 is within 1000 of being a square. Is there another n such that n!+1 <= "1000 away" from being a perfect square? LINKS Amiram Eldar, Table of n, a(n) for n = 1..808 P. Leyland, Solutions to n!+1=m^2. EXAMPLE a(5)=0 because 5!+1 is a square. a(8)=80 because 8!+1 = 40321 and the next larger square is 40401, so 40401-40321 = 80. MATHEMATICA a[n_] := Ceiling @ Sqrt[(f = n! + 1)]^2 - f; Array[a, 27] (* Amiram Eldar, Dec 14 2019 *) PROG (PARI) for(k=1, 27, print1(ceil(sqrt(k!+1))^2-(k!+1), ", ")) \\ Hugo Pfoertner, Dec 14 2019 CROSSREFS Cf. A038507, A087374. Sequence in context: A317741 A317902 A317871 * A079549 A143374 A277899 Adjacent sequences:  A082992 A082993 A082994 * A082996 A082997 A082998 KEYWORD nonn AUTHOR Jason Earls, May 29 2003 STATUS approved

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Last modified June 25 20:02 EDT 2022. Contains 354851 sequences. (Running on oeis4.)