A195098 -id:A195098 - cp's OEIS frontend

A195099 Inverse permutation of A195098; every positive integer occurs exactly once.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 14, 16, 17, 18, 20, 21, 19, 22, 23, 24, 26, 27, 28, 25, 29, 30, 31, 33, 34, 35, 36, 32, 37, 38, 39, 41, 42, 43, 45, 44, 40, 46, 47, 48, 50, 51, 52, 54, 55, 53, 49, 56, 57, 58, 60, 61, 62, 64, 65, 66, 63, 59, 67, 68, 69

Offset: 1

Clark Kimberling, Sep 08 2011

nonn

Cf. A194098, A195097, A194959.

Mathematica
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(See A195098.)
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A195097 Fractalization of (1+[3n/4]), where [ ] = floor.

Original entry on oeis.org

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

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+[3n/4]) is a subsequence ofy A037915.

Cf. A194959, A002265, A195098, A195099.

r = 3/4; p[n_] := 1 + Floor[n*r] (* A037915 *)
Table[p[n], {n, 1, 90}]
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]    (* A195097 *)
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}]](* A195098 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]](* A195099 *)

cp's OEIS Frontend

A195099 Inverse permutation of A195098; every positive integer occurs exactly once.

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