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A194899
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Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=sqrt(12).
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4
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1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 5, 3, 1, 4, 2, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2, 13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2
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OFFSET
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1,3
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COMMENTS
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See A194832 for a general discussion.
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LINKS
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EXAMPLE
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First nine rows:
1
1 2
3 1 2
3 1 4 2
5 3 1 4 2
5 3 1 6 4 2
7 5 3 1 6 4 2
7 5 3 1 8 6 4 2
9 7 5 3 1 8 6 4 2
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MATHEMATICA
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r = Sqrt[12];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]] (* A194899 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 15},
q[n_] := Position[p, n]; Flatten[Table[q[n],
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PROG
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(PARI) row(n) = Vec(vecsort(vector(n, k, frac(k*sqrt(12))), , 1));
tabl(nn) = for (n=1, nn, print(row(n))); \\ Michel Marcus, Feb 06 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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