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Search: id:A003135
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| A003135 |
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n! is a nontrivial product of factorials. It is conjectured that the list is complete. |
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+0
11
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OFFSET
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1,1
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COMMENT
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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 (j.mccranie(AT)comcast.net), Jun 15 2005
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REFERENCES
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P. Erdos, 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.
R. K. Guy, "Unsolved Problems in Number Theory", section B23.
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LINKS
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Index entries for sequences related to factorial numbers
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EXAMPLE
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16! = 14! * 5! * 2!, and 14 < 16-1, so 16 is in the sequence.
9! = 2! * 3! * 3! * 7!
10! = 6! * 7! or 10! = 3! * 5! * 7!.
16! = 2! * 5! * 14!
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CROSSREFS
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Cf. A034878, A001013, A058295, A075082, A109095, A109096, A109097, A109098.
Adjacent sequences: A003132 A003133 A003134 this_sequence A003136 A003137 A003138
Sequence in context: A099616 A140209 A073829 this_sequence A105742 A105834 A121061
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KEYWORD
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nonn,bref,more
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AUTHOR
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njas
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