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 A194905 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=Pi. 6
 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 9, 2, 3, 4, 5, 6, 7, 8, 1, 9, 2, 10, 3, 4, 5, 6, 7, 8, 1, 9, 2, 10, 3, 11, 4, 5, 6, 7, 8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 6, 7, 8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 7, 8, 1, 9 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS See A194832 for a general discussion. LINKS EXAMPLE First nine rows: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 9 2 3 4 5 6 7 MATHEMATICA r = Pi; t[n_] := Table[FractionalPart[k*r], {k, 1, n}]; f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194905 *) 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}]]  (* A194906 *) q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194907 *) CROSSREFS Cf. A194832, A194906, A194907. Sequence in context: A140756 A002260 A243732 * A243730 A133994 A066041 Adjacent sequences:  A194902 A194903 A194904 * A194906 A194907 A194908 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 05 2011 STATUS approved

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Last modified September 18 18:55 EDT 2021. Contains 347533 sequences. (Running on oeis4.)