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 A194859 Triangular array (and fractal sequence):  row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {e}, {2e}, ..., {ne}. 4
 1, 2, 1, 3, 2, 1, 3, 2, 1, 4, 3, 2, 5, 1, 4, 3, 6, 2, 5, 1, 4, 7, 3, 6, 2, 5, 1, 4, 7, 3, 6, 2, 5, 1, 8, 4, 7, 3, 6, 2, 9, 5, 1, 8, 4, 7, 3, 10, 6, 2, 9, 5, 1, 8, 4, 7, 3, 10, 6, 2, 9, 5, 1, 8, 4, 11, 7, 3, 10, 6, 2, 9, 5, 12, 1, 8, 4, 11, 7, 3, 10, 6, 13, 2, 9, 5, 12, 1, 8, 4, 11, 7, 14, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A194832 for a general discussion. LINKS EXAMPLE First nine rows: 1 2 1 3 2 1 3 2 1 4 3 2 5 1 4 3 6 2 5 1 4 7 3 6 2 5 1 4 7 3 6 2 5 1 8 4 7 3 6 2 9 5 1 8 4 MATHEMATICA r = E; t[n_] := Table[FractionalPart[k*r], {k, 1, n}]; f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194859 *) 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, 13}, {k, 1, n}]]  (* A194860 *) q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194861 *) CROSSREFS Cf. A194832, A194860, A194861. Sequence in context: A174737 A131756 A212620 * A194838 A085014 A082074 Adjacent sequences:  A194856 A194857 A194858 * A194860 A194861 A194862 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 04 2011 STATUS approved

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Last modified February 21 01:08 EST 2019. Contains 320363 sequences. (Running on oeis4.)