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

Author

Rémy Sigrist, Aug 09 2022

Keywords

• nonn
• base
• easy

Comments

This sequence is unbounded (see also A356516).

Examples

			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.
		

Crossrefs

Cf. A000120, A053735, A356384, A356516.

Programs

PARI

a(n) = { for (b=2, oo, if (n
				

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

Formula

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