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
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.
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).
Comments