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A065369
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Replace 3^k with (-3)^k in ternary expansion of n.
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13
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0, 1, 2, -3, -2, -1, -6, -5, -4, 9, 10, 11, 6, 7, 8, 3, 4, 5, 18, 19, 20, 15, 16, 17, 12, 13, 14, -27, -26, -25, -30, -29, -28, -33, -32, -31, -18, -17, -16, -21, -20, -19, -24, -23, -22, -9, -8, -7, -12, -11, -10, -15, -14, -13, -54, -53, -52, -57, -56, -55, -60, -59, -58, -45, -44, -43, -48, -47, -46
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OFFSET
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0,3
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COMMENTS
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Base 3 representation for n (in lexicographic order) converted from base -3 to base 10.
Notation: (3)[n](-3)
Fixed point of the morphism 0-> 0,1,2 ; 1-> -3,-2,-1 ; 2-> -6,-5,-4 ; ...; n-> -3n,-3n+1,-3n+2. - Philippe Deléham, Oct 22 2011
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LINKS
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FORMULA
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a(3*k+m) = -3*a(k)+m for 0 <= m < 3. - Chai Wah Wu, Jan 16 2020
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EXAMPLE
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15 = +1(9)+2(3)+0(1) -> +1(+9)+2(-3)+0(+1) = +3 = a(15)
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MATHEMATICA
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f[n_Integer, b_Integer] := Block[{l = IntegerDigits[n]}, Sum[l[[ -i]]*(-b)^(i - 1), {i, 1, Length[l]}]]; a = Table[ FromDigits[ IntegerDigits[n, 3]], {n, 0, 80}]; b = {}; Do[b = Append[b, f[a[[n]], 3]], {n, 1, 80}]; b
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PROG
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(PARI) a(n) = fromdigits(digits(n, 3), -3) \\ Rémy Sigrist, Feb 06 2020
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CROSSREFS
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Cf. A007089, A053985, A065367, A073785, A073791, A073792, A073793, A073794, A073795, A073796, A073835.
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KEYWORD
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AUTHOR
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STATUS
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approved
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