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A093347
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A 3-fractal "castle" starting with 0.
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10
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0, 1, 0, 3, 2, 3, 0, 1, 0, 9, 8, 9, 6, 7, 6, 9, 8, 9, 0, 1, 0, 3, 2, 3, 0, 1, 0, 27, 26, 27, 24, 25, 24, 27, 26, 27, 18, 19, 18, 21, 20, 21, 18, 19, 18, 27, 26, 27, 24, 25, 24, 27, 26, 27, 0, 1, 0, 3, 2, 3, 0, 1, 0, 9, 8, 9, 6, 7, 6, 9, 8, 9, 0, 1, 0, 3, 2, 3, 0, 1, 0, 81, 80, 81, 78, 79, 78, 81
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OFFSET
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1,4
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LINKS
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FORMULA
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a(1) = 0 then a(n) = w(n) - a(n-w(n)) where w(n) = 3^floor(log(n-1)/log(3)).
a(3^n) = 0, a(3^n+1) = 3^n, a(3^n+2) = 3^n-1, a(3^n+3) = 3^n, etc.
a(n) = Sum_{i=1..n-1} (-1)^(i-1)*3^valuation(i, 3).
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MATHEMATICA
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a[n_] := Sum[(-1)^(i+1) * 3^IntegerExponent[i, 3], {i, 1, n-1}]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)
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PROG
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(PARI) a(n)=if(n<2, 0, 3^floor(log(n-1)/log(3))-a(n-3^floor(log(n-1)/log(3))))
(PARI) a(n) = my(s=-1); fromdigits([if(d==1, s=-s) |d<-digits(n-1, 3)], 3); \\ Kevin Ryde, Jan 01 2024
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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