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A321883
Nonnegative integers n for which n! + 1 is not a square.
0
0, 1, 2, 3, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69
OFFSET
1,3
COMMENTS
Complement of A146968 = positive integers n such that n!+1 is a square (Brocard's problem, so far {4, 5, 7} are the only known terms).
A weak form of Szpiro's conjecture implies that there are only finitely many nonnegative integers that are not in the sequence (cf. Overholt, 1993).
LINKS
B. C. Berndt and W. F. Galway, On the Brocard-Ramanujan Diophantine Equation n! + 1 = m^2, The Ramanujan Journal, Vol. 4, No. 1 (2000), 41-42.
M. Overholt, The Diophantine Equation n! + 1 = m^2, Bulletin of the London Mathematical Society, Vol. 25, No. 2 (1993), 104.
MATHEMATICA
Select[Range[0, 100], !IntegerQ[Sqrt[#!+1]] &] (* Amiram Eldar, Nov 21 2018 *)
PROG
(PARI) select( is(n)=!issquare(n!+1), [0..99]) \\ M. F. Hasler, Nov 20 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Nov 20 2018
STATUS
approved