A195108 -id:A195108 - cp's OEIS frontend

A195109 Inverse permutation of A195108; every positive integer occurs exactly once.

1, 2, 3, 6, 4, 5, 9, 7, 10, 8, 13, 15, 11, 14, 12, 21, 18, 20, 16, 19, 17, 27, 24, 26, 28, 22, 25, 23, 34, 31, 36, 33, 35, 29, 32, 30, 42, 45, 39, 44, 41, 43, 37, 40, 38, 55, 51, 54, 48, 53, 50, 52, 46, 49, 47, 65, 61, 64, 58, 66, 63, 60, 62, 56, 59, 57, 76, 72, 75

Offset: 1

Clark Kimberling, Sep 09 2011

nonn

Cf. A195108, A195107, A004736, A194959, A195110.

Mathematica
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(See A195108.)
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A195107 Fractalization of the fractal sequence A004736. Interspersion fractally induced by A004736.

Original entry on oeis.org

1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 3, 5, 1, 4, 2, 6, 3, 5, 1, 4, 2, 6, 3, 5, 7, 1, 4, 2, 6, 3, 8, 5, 7, 1, 4, 2, 6, 9, 3, 8, 5, 7, 1, 4, 2, 10, 6, 9, 3, 8, 5, 7, 1, 4, 2, 10, 6, 9, 3, 11, 8, 5, 7, 1, 4, 2, 10, 6, 9, 12, 3, 11, 8, 5, 7, 1, 4, 2, 10, 6, 13, 9, 12, 3, 11, 8, 5, 7, 1, 4, 2, 10, 14

Offset: 1

Clark Kimberling, Sep 09 2011

nonn

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence A004736 is the fractal sequence obtained by concatenating the segments 1; 2,1; 3,2,1; 4,3,2,1;...

Cf. A194959, A004736, A195108, A195109.

j[n_] := Table[n + 1 - k, {k, 1, n}]; t[1] = j[1];
t[n_] := Join[t[n - 1], j[n]]   (* A004736 *)
t[10]
p[n_] := t[20][[n]]
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
f[20] (* A195107 *)
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},
{k, 1, n}]] (* A195108 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195109 *)

cp's OEIS Frontend

A195109 Inverse permutation of A195108; every positive integer occurs exactly once.

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