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A195073
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Fractalization of (n-[n/sqrt(3)]), where [ ]=floor.
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4
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1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 2, 4, 5, 3, 1, 2, 4, 6, 5, 3, 1, 2, 4, 7, 6, 5, 3, 1, 2, 4, 7, 8, 6, 5, 3, 1, 2, 4, 7, 9, 8, 6, 5, 3, 1, 2, 4, 7, 9, 10, 8, 6, 5, 3, 1, 2, 4, 7, 9, 11, 10, 8, 6, 5, 3, 1, 2, 4, 7, 9, 11, 12, 10, 8, 6, 5, 3, 1, 2, 4, 7, 9, 11, 13, 12, 10, 8, 6, 5, 3, 1, 2, 4, 7, 9
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OFFSET
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1,2
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COMMENTS
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See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (n-[n/sqrt(3)]) is A195072.
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LINKS
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MATHEMATICA
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r = Sqrt[3]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}] (* A195072 *)
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
row[n_] := Position[f[30], n];
u = TableForm[Table[row[n], {n, 1, 5}]]
v[n_, k_] := Part[row[n], k];
w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
q[n_] := Position[w, n]; Flatten[
Table[q[n], {n, 1, 80}]] (* A195075 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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