A356384 For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) = x_n(b-1) minus the sum of digits of x_n(b-1) in base b; a(n) is the least b such that x_n(b) = 0.

1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13

Offset: 0

Author

Rémy Sigrist, Aug 05 2022

Keywords

• nonn
• base

Comments

This sequence is well defined: for any n >= 0: if x_n(b) > 0, then x_n(b+1) < x_n(b), and we must eventually reach 0.

This sequence is weakly increasing; this is related to the fact that for any base b > 1, k -> (k minus the sum of digits of k in base b) is weakly increasing.

Note that some values (like 7) do not appear in this sequence (see also A356386).

Examples

			For n = 42:
- we have:
      b  x(b)
      -  ----
      1    42
      2    39
      3    36
      4    33
      5    28
      6    20
      7    12
      8     7
      9     0
- so a(42) = 9.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, Colored scatterplot of (n, x_n(b)) for n <= 1000 and b = 1..a(n) (the color is function of b)
• Rémy Sigrist, PARI program

Crossrefs

Cf. A011371, A066568, A071542, A261231, A344853, A356386.

Programs

PARI

See Links section.