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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).

%I A356515 #7 Aug 12 2022 12:37:31
%S A356515 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 A356515 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 A356515 2,1,1,2,2,1,1,2,1,2,2,3,2,1,1,2,1,2,2
%N 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).
%C A356515 This sequence is unbounded (see also A356516).
%F A356515 a(2*n) = a(n).
%e A356515 For n = 87:
%e A356515 - we have:
%e A356515      b    x_87(b)  x_87(b) in base b+1
%e A356515      ---  -------  -------------------
%e A356515        1       87            "1010111"
%e A356515        2        5                 "12"
%e A356515      >=3        3                  "3"
%e A356515 - so a(87) = 3.
%o A356515 (PARI) a(n) = { for (b=2, oo, if (n<b, return (n), n=sumdigits(n,b))) }
%o A356515 (Python)
%o A356515 from sympy.ntheory import digits
%o A356515 def a(n):
%o A356515     xn, b = n, 2
%o A356515     while xn >= b: xn = sum(digits(xn, b)[1:]); b += 1
%o A356515     return xn
%o A356515 print([a(n) for n in range(105)]) # _Michael S. Branicky_, Aug 10 2022
%Y A356515 Cf. A000120, A053735, A356384, A356516.
%K A356515 nonn,base,easy
%O A356515 0,4
%A A356515 _Rémy Sigrist_, Aug 09 2022