OFFSET
1,1
COMMENTS
See A269982 for a definition of factorial fractility and a guide to related sequences.
LINKS
Robert Price, Table of n, a(n) for n = 1..67
EXAMPLE
NI(1/5) = (2, 3, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 2, ...)
NI(2/5) = (2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...)
NI(3/5) = (1, 2, 3, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, ...)
NI(4/5) = (1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, ...)
so there are 2 equivalences classes for n = 5, and the fractility of 5 is 2.
MATHEMATICA
A269982[n_] := CountDistinct[With[{l = NestWhileList[
Rescale[#, {1/(Floor[x] + 1)!, 1/Floor[x]!} /.
FindRoot[1/x! == #, {x, 1}]] &, #, UnsameQ, All]},
Min@l[[First@First@Position[l, Last@l] ;; ]]] & /@
Range[1/n, 1 - 1/n, 1/n]]; (* Davin Park, Nov 19 2016 *)
Select[Range[2, 500], A269982[#] == 2 &] (* Robert Price, Sep 19 2019 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling and Peter J. C. Moses, Mar 11 2016
EXTENSIONS
Edited by M. F. Hasler, Nov 05 2018
STATUS
approved