A269988 Numbers k having factorial fractility A269982(k) = 6.

94, 105, 115, 141, 142, 153, 170, 175, 182, 184, 187, 189, 196, 205, 207, 210, 212, 213, 215, 221, 225, 235, 245, 252, 254, 255, 260, 265, 275, 276, 282, 290, 299, 306, 314, 325, 367, 368, 370, 378, 381, 388, 392, 399, 414, 424, 425, 426, 434, 435, 446, 450

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..60

Example

NI(1/94) = (4, 3, 2, 3, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, 3, 1, 4, 1, 1, 2, ...),
NI(2/94) = (4, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, ...),
NI(4/94) = (3, 5, 1, 1, 2, 2, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, ...),
NI(7/94) = (3, 2, 2, 2, 1, 2, 4, 3, 2, 3, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, ...),
NI(11/94) = (3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, ...),
NI(47/94) = (2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...):
These 6 equivalence classes represent all the classes for k = 94, so the factorial fractility of 94 is 6.

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[#] == 6 &] (* Robert Price, Sep 19 2019 *)

Prog

(PARI) select( is_A269988(n)=A269982(n)==6, [1..400]) \\ M. F. Hasler, Nov 05 2018

Crossrefs

Cf. A000142 (factorial numbers), A269982 (factorial fractility of n); A269983, A269984, A269985, A269986, A269987 (numbers with factorial fractility 1, 2, ..., 5, respectively).

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

Sequence in context: A020444 A045301 A146336 * A044974 A257525 A020355

Adjacent sequences: A269985 A269986 A269987 * A269989 A269990 A269991

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