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..70
EXAMPLE
NI(1/68) = (4, 2, 3, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, ...)
NI(4/68) = (3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, ...)
NI(6/68) = (3, 2, 1, 2, 2, 3, 1, 2, 3, 1, 1, 2, 1, 2, 2, 3, 1, 2, 3, ...)
NI(17/68) = (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...)
NI(34/68) = (2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...).
These 5 equivalence classes represent all the classes for n = 68, so the factorial fractility of 68 is 5.
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[#] == 5 &] (* Robert Price, Sep 19 2019 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling and Peter J. C. Moses, Mar 11 2016
EXTENSIONS
Edited and more terms added by M. F. Hasler, Nov 05 2018
STATUS
approved