A194918 -id:A194918 - cp's OEIS frontend

A194919 Inverse permutation of A194918; 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, 35, 36, 34, 32, 31, 29, 38, 41, 43, 45, 44, 42, 40, 39, 37, 47, 50, 52, 55, 54, 53, 51, 49, 48, 46, 57, 60, 62, 65, 66, 64, 63, 61, 59, 58, 56, 68, 71, 73

Offset: 1

Clark Kimberling, Sep 08 2011

nonn

Cf. A194918, A194917, A189663, A194959.

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(See A194918.)
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A194917 Fractalization of (n-[nr-n]), where [ ]=floor and r=(1+sqrt(5))/2 (the golden ratio).

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

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 (n-[nr-n]) is A189663.

Cf. A194959, A189663, A194918, A194919.

r = GoldenRatio; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A189663 *)
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] (*  A194917 *)
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}]] (* A194918 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194919 *)

cp's OEIS Frontend

A194919 Inverse permutation of A194918; every positive integer occurs exactly once.

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