A373085 Numbers k such that the factorial base representation of 1/k without the leading zeros is palindromic.

1, 2, 3, 6, 8, 9, 10, 12, 20, 24, 30, 40, 60, 120, 126, 144, 160, 180, 189, 210, 240, 315, 360, 384, 630, 720, 840, 896, 1008, 1056, 1120, 1260, 1680, 2240, 2520, 4480, 5040, 5184, 5760, 6048, 6300, 6720, 6912, 8064, 9072, 9450, 10080, 12096, 13440, 14400, 18144

Offset

1,2

Comments

All the factorials (A000142) are terms, since the factorial base representation of 1/k! is k-1 0's followed by 1.

If k > 4 is composite then (k-1)!/k is a term.

Links

Table of n, a(n) for n=1..51.

Wikipedia, Factorial number system (Fractional values).

Index entries for sequences related to factorial base representation.

Example

The first 10 terms are:
   n  a(n)   1/a(n) in factorial base
  --  ----   ------------------------
   1    1    1.
   2    2    0.1
   3    3    0.02
   4    6    0.01
   5    8    0.003
   6    9    0.00232
   7   10    0.0022
   8   12    0.002
   9   20    0.0011
  10   24    0.001

Mathematica

q[n_] := Module[{d = NumberDecompose[1/n, 1/Range[n]!], i}, i = Position[d, _?(# > 0&)] // Flatten; PalindromeQ[d[[First[i];; Last[i]]]]]; q[1] = True; Select[Range[1000], q]

Crossrefs

Cf. A000142, A007623, A046807, A294168.

Sequence in context: A175904 A084090 A353988 * A047286 A344156 A344166

Adjacent sequences: A373082 A373083 A373084 * A373086 A373087 A373088

Keyword

nonn,base

Author

Amiram Eldar, May 23 2024

Status

approved