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 A054073 Fractal sequence induced by sqrt(2): for k >= 1 let p(k) be the permutation of 1,2,...,k obtained by ordering the fractional parts {h*sqrt(2)} for h=1,2,...,k; then juxtapose p(1),p(2),p(3),... 7
 1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 5, 3, 1, 4, 2, 5, 3, 1, 6, 4, 2, 5, 3, 1, 6, 4, 2, 7, 5, 3, 8, 1, 6, 4, 2, 7, 5, 3, 8, 1, 6, 4, 9, 2, 7, 5, 10, 3, 8, 1, 6, 4, 9, 2, 7, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 13, 1, 6, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A054073 generates the interspersion A054077; see A194832 and the Mathematica program. LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 EXAMPLE p(1)=(1); p(2)=(1,2); p(3)=(3,1,2); p(4)=(3,1,4,2). When formatted as a triangle, the first 9 rows: 1 1 2 3 1 2 3 1 4 2 5 3 1 4 2 5 3 1 6 4 2 5 3 1 6 4 2 7 5 3 8 1 6 4 2 7 5 3 8 1 6 4 9 2 7 MATHEMATICA r = Sqrt[2]; t[n_] := Table[FractionalPart[k*r], {k, 1, n}]; f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]] (* A054073 *) 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}]] (* A054077 *) q[n_] := Position[p, n]; Flatten[ Table[q[n], {n, 1, 80}]]  (* A054076 *) (* Clark Kimberling, Sep 03 2011 *) CROSSREFS Cf. A054071, A054072, A194832. Sequence in context: A194862 A194832 A195107 * A194871 A194899 A228094 Adjacent sequences:  A054070 A054071 A054072 * A054074 A054075 A054076 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 19 00:22 EST 2022. Contains 350464 sequences. (Running on oeis4.)