|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|