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

Author

Amiram Eldar, May 23 2024

Keywords

• nonn
• base

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.

Examples

			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
		

Links

• Wikipedia, Factorial number system (Fractional values).
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A000142, A007623, A046807, A294168.

Programs

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]