A343506 Numbers k such that the largest digit in the factorial base expansion of 1/k is 1.

1, 2, 6, 20, 24, 120, 630, 720, 4480, 5040, 36288, 40320, 362880, 3326400, 3628800, 39916800

Offset: 1

Author

Rémy Sigrist, Apr 17 2021

Keywords

• nonn
• base
• more

Comments

Equivalently these are the numbers k such that A299020(k) = 1 or A343505(k) = 1.

This sequence is infinite as it contains:

- the factorial numbers (A000142),

- 1/(1/A060462(k)! + 1/(A060462(k)-1)!) for k > 2,

- 1/(1/A120416(k)! + 1/(A120416(k)-1)! + 1/(A120416(k)-2)!) for k > 0.

Examples

			The first terms, alongside the factorial base expansion of their inverse, are:
  n   a(n)     1/a(n) in factorial base
  --  -------  ------------------------
   1        1  1
   2        2  0.1
   3        6  0.0 1
   4       20  0.0 0 1 1
   5       24  0.0 0 1
   6      120  0.0 0 0 1
   7      630  0.0 0 0 0 1 1
   8      720  0.0 0 0 0 1
   9     4480  0.0 0 0 0 0 1 1
  10     5040  0.0 0 0 0 0 1
  11    36288  0.0 0 0 0 0 0 1 1
  12    40320  0.0 0 0 0 0 0 1
  13   362880  0.0 0 0 0 0 0 0 1
  14  3326400  0.0 0 0 0 0 0 0 0 1 1
  15  3628800  0.0 0 0 0 0 0 0 0 1
		

Links

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

Crossrefs

Cf. A000142, A060462, A120416, A294168, A299020, A343505.

Cf. A333402 (decimal).

Programs

PARI

is(n) = my (f=1/n); for (r=2, oo, if (f==0, return (1), floor(f)>1, return (0), f=frac(f)*r))