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A003135 n! is a nontrivial product of factorials. It is conjectured that the list is complete. 11
9, 10, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A "nontrivial" solution is one in which the largest x! in the product of a(n)! is such that x < a(n)-1. There are no other terms < 10^5. - Jud McCranie, Jun 15 2005
REFERENCES
R. K. Guy, "Unsolved Problems in Number Theory", section B23.
LINKS
P. Erdős, Problems and results on number theoretic properties of consecutive integers and related questions, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 25-44.
EXAMPLE
9! = 2! * 3! * 3! * 7! and 7 < 9-1, so 9 is in the sequence.
10! = 6! * 7! or 10! = 3! * 5! * 7! and 7 < 10-1, so 10 is in the sequence.
16! = 2! * 5! * 14! and 14 < 16-1, so 16 is in the sequence.
CROSSREFS
Sequence in context: A197113 A099616 A073829 * A105742 A105834 A280846
KEYWORD
nonn,bref,more,hard
AUTHOR
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)