A221861 The least number k that maximizes k! mod n.
0, 0, 2, 2, 4, 2, 3, 3, 3, 3, 5, 3, 12, 4, 4, 4, 16, 5, 9, 3, 5, 6, 14, 3, 4, 4, 4, 4, 18, 4, 30, 4, 6, 9, 4, 4, 36, 6, 8, 4, 40, 5, 21, 5, 5, 10, 23, 4, 7, 7, 10, 7, 52, 8, 9, 6, 13, 7, 15, 4, 8, 14, 5, 5, 5, 6, 18, 8, 17, 5, 7, 5, 72, 21, 5, 14, 9, 8, 23, 5
Offset: 1
Keywords
Examples
For n=11, we see that the factorial of 5 (120), modulo 11 is 10, which is the highest possible value, so the 11th term is 5.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A062170.
Programs
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Ruby
(1..100).map{|n|(0..n).max_by{|x|[(1..x).inject(1,:*)%n,-x]}}