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A065368
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Alternating sum of ternary digits in n. Replace 3^k with (-1)^k in ternary expansion of n.
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10
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0, 1, 2, -1, 0, 1, -2, -1, 0, 1, 2, 3, 0, 1, 2, -1, 0, 1, 2, 3, 4, 1, 2, 3, 0, 1, 2, -1, 0, 1, -2, -1, 0, -3, -2, -1, 0, 1, 2, -1, 0, 1, -2, -1, 0, 1, 2, 3, 0, 1, 2, -1, 0, 1, -2, -1, 0, -3, -2, -1, -4, -3, -2, -1, 0, 1, -2, -1, 0, -3, -2, -1, 0, 1, 2, -1, 0, 1, -2, -1, 0, 1, 2, 3, 0, 1, 2, -1, 0, 1, 2, 3, 4, 1, 2, 3, 0, 1, 2, 3, 4, 5, 2, 3
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OFFSET
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0,3
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COMMENTS
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Notation: (3)[n](-1).
Fixed point of the morphism 0 -> 0,1,2; 1 -> -1,0,1; 2 -> -2,-1,0; ...; n -> -n,-n+1,-n+2. - Philippe Deléham, Oct 22 2011
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(x) = x * (1 + 2*x) / (1 - x^3) - (1 + x + x^2) * A(x^3). - Ilya Gutkovskiy, Jul 28 2021
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EXAMPLE
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15 = +1(9)+2(3)+0(1) -> +1(+1)+2(-1)+0(+1) = -1 = a(15).
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PROG
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(Python)
from sympy.ntheory.digits import digits
def a(n):
return sum(bi*(-1)**k for k, bi in enumerate(digits(n, 3)[1:][::-1]))
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CROSSREFS
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KEYWORD
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base,easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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