A195077 -id:A195077 - cp's OEIS frontend

A195078 Inverse permutation of A195077; every positive integer occurs exactly once.

1, 3, 2, 5, 6, 4, 8, 10, 9, 7, 12, 15, 14, 13, 11, 17, 20, 21, 19, 18, 16, 23, 26, 28, 27, 25, 24, 22, 30, 33, 36, 35, 34, 32, 31, 29, 38, 41, 44, 45, 43, 42, 40, 39, 37, 47, 50, 53, 55, 54, 52, 51, 49, 48, 46, 57, 60, 63, 66, 65, 64, 62, 61, 59, 58, 56, 68, 71, 74

Offset: 1

Clark Kimberling, Sep 08 2011

nonn

Not the same as A194916.

Cf. A195077, A195076.

Mathematica
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(See A195077.)
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A195076 Fractalization of (1+[n/3]), where [ ]=floor.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Sep 08 2011

nonn

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[n/3]) is A009620. A195076 is not identical to A194914.

Cf. A195076, A195077, A195078.

r = 3; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A009620 *)
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] (* A195076 *)
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}]]  (* A195077 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A195078 *)

cp's OEIS Frontend

A195078 Inverse permutation of A195077; every positive integer occurs exactly once.

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