A356384 - OEIS

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

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OFFSET

0,2

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).

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

EXAMPLE

For n = 42:

- we have:

b x(b)

- ----

1 42

2 39