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A269987 Numbers n having factorial fractility A269982(n) = 5. 7
68, 70, 71, 85, 92, 100, 126, 127, 130, 136, 138, 145, 154, 157, 161, 164, 168, 180, 185, 195, 200, 204, 220, 224, 232, 247, 253, 266, 272, 288, 291, 300, 304, 310, 318, 324, 328, 333, 334, 336, 341, 342, 348, 360, 365, 369, 371, 390, 395, 400, 404, 407, 408, 412, 418, 433, 440, 441, 443, 444, 447 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A269982 for a definition of factorial fractility and 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 that 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]]; (* from Davin Park, Nov 19 2016 *)

Select[Range[2, 500], A269982[#] == 5 &] (* Robert Price, Sep 19 2019 *)

PROG

(PARI) select( is_A269987(n)=A269982(n)==5, [1..400]) \\ M. F. Hasler, Nov 05 2018

CROSSREFS

Cf. A000142 (factorial numbers), A269982 (factorial fractility of n); A269983, A269984, A269985, A269986, A269988 (numbers with factorial fractility 1, 2, ..., 6, respectively).

Cf. A269570 (binary fractility), A270000 (harmonic fractility).

Sequence in context: A043854 A043862 A043871 * A058906 A130694 A269748

Adjacent sequences:  A269984 A269985 A269986 * A269988 A269989 A269990

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

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Last modified June 14 12:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)