%I #7 Aug 12 2022 12:37:31
%S 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,
%T 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,
%U 2,1,1,2,2,1,1,2,1,2,2,3,2,1,1,2,1,2,2
%N 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).
%C This sequence is unbounded (see also A356516).
%F a(2*n) = a(n).
%e For n = 87:
%e - we have:
%e b x_87(b) x_87(b) in base b+1
%e --- ------- -------------------
%e 1 87 "1010111"
%e 2 5 "12"
%e >=3 3 "3"
%e - so a(87) = 3.
%o (PARI) a(n) = { for (b=2, oo, if (n<b, return (n), n=sumdigits(n,b))) }
%o (Python)
%o from sympy.ntheory import digits
%o def a(n):
%o xn, b = n, 2
%o while xn >= b: xn = sum(digits(xn, b)[1:]); b += 1
%o return xn
%o print([a(n) for n in range(105)]) # _Michael S. Branicky_, Aug 10 2022
%Y Cf. A000120, A053735, A356384, A356516.
%K nonn,base,easy
%O 0,4
%A _Rémy Sigrist_, Aug 09 2022