A356515 For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) is the sum of digits of x_n(b-1) in base b; x_n is eventually constant, with value a(n).

0, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 3, 2, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 3, 2, 1, 1, 2, 1, 2, 2

Offset

0,4

Comments

This sequence is unbounded (see also A356516).

Links

Table of n, a(n) for n=0..86.

Formula

a(2*n) = a(n).

Example

For n = 87:
- we have:
     b    x_87(b)  x_87(b) in base b+1
     ---  -------  -------------------
       1       87            "1010111"
       2        5                 "12"
     >=3        3                  "3"
- so a(87) = 3.

Prog

(PARI) a(n) = { for (b=2, oo, if (n<b, return (n), n=sumdigits(n, b))) }
(Python)
from sympy.ntheory import digits
def a(n):
    xn, b = n, 2
    while xn >= b: xn = sum(digits(xn, b)[1:]); b += 1
    return xn
print([a(n) for n in range(105)]) # Michael S. Branicky, Aug 10 2022

Crossrefs

Cf. A000120, A053735, A356384, A356516.

Sequence in context: A265918 A207676 A161175 * A095955 A272772 A293431

Adjacent sequences: A356512 A356513 A356514 * A356516 A356517 A356518

Keyword

nonn,base,easy

Author

Rémy Sigrist, Aug 09 2022

Status

approved