A195114 -id:A195114 - cp's OEIS frontend

A195115 Inverse permutation of A195114; every positive integer occurs exactly once.

1, 3, 2, 5, 6, 4, 8, 9, 10, 7, 15, 12, 13, 14, 11, 20, 21, 17, 18, 19, 16, 26, 27, 28, 23, 24, 25, 22, 33, 34, 35, 36, 30, 31, 32, 29, 45, 41, 42, 43, 44, 38, 39, 40, 37, 54, 55, 50, 51, 52, 53, 47, 48, 49, 46, 64, 65, 66, 60, 61, 62, 63, 57, 58, 59, 56, 75, 76, 77

Offset: 1

Clark Kimberling, Sep 09 2011

nonn

Cf. A195114, A195113, A194954.

Mathematica
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(See A195114.)
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A195113 Fractalization of the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Sep 09 2011

nonn

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence p; for the present case, p is the concatenation of the segments 1, 123,1234,12345,123456,..., so that p is obtained from A002260 by deleting the segment 12.

Cf. A194959, A002260, A195114, A195115.

j[n_] := Table[k, {k, 1, n}];
t[1] = j[1]; t[2] = j[1];
t[n_] := Join[t[n - 1], j[n]] (* A002260; initial 1,1,2 repl by 1 *)
t[12]
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]  (* A195113 *)
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}]] (* A195114 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A195115 *)

cp's OEIS Frontend

A195115 Inverse permutation of A195114; every positive integer occurs exactly once.

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