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A356515
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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).
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1
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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
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OFFSET
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0,4
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COMMENTS
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This sequence is unbounded (see also A356516).
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LINKS
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FORMULA
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a(2*n) = a(n).
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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