cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A195111 Interspersion fractally induced by the fractal sequence A002260.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 10, 8, 9, 7, 15, 13, 14, 11, 12, 21, 19, 20, 16, 17, 18, 28, 26, 27, 23, 24, 25, 22, 36, 34, 35, 31, 32, 33, 29, 30, 45, 43, 44, 40, 41, 42, 37, 38, 39, 55, 53, 54, 50, 51, 52, 46, 47, 48, 49, 66, 64, 65, 61, 62, 63, 57, 58, 59, 60, 56, 78, 76, 77
Offset: 1

Views

Author

Clark Kimberling, Sep 09 2011

Keywords

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.
Every pair of rows eventually intersperse. As a sequence, A194111 is a permutation of the positive integers, with inverse A195129.
The sequence A002260 is the fractal sequence obtained by concatenating the segments 1; 12; 123; 1234; 12345;...

Examples

			Northwest corner:
1...3...6...10..15..21..28..36..45
2...4...8...13..19..26..34..43..53
5...9...14..20..27..35..44..54..65
7...11..16..23..31..40..50..61..73
12..17..24..32..41..51..62..74..87

Crossrefs

Cf. A194959, A002260, A195110, A195112.

Programs

  • Mathematica
    j[n_] := Table[k, {k, 1, n}]; t[1] = j[1];
t[n_] := Join[t[n - 1], j[n]]   (* A002260 *)
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] (* A195110 *)
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}]] (* A195111 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
  {n, 1, 80}]]  (* A195112 *)

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 09 2011

Keywords

Crossrefs

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

Programs

A195112 Inverse permutation of A195111; every positive integer occurs exactly once.

Original entry on oeis.org

1, 3, 2, 5, 6, 4, 10, 8, 9, 7, 14, 15, 12, 13, 11, 19, 20, 21, 17, 18, 16, 28, 25, 26, 27, 23, 24, 22, 35, 36, 32, 33, 34, 30, 31, 29, 43, 44, 45, 40, 41, 42, 38, 39, 37, 52, 53, 54, 55, 49, 50, 51, 47, 48, 46, 66, 62, 63, 64, 65, 59, 60, 61, 57, 58, 56, 77, 78, 73
Offset: 1

Views

Author

Clark Kimberling, Sep 09 2011

Keywords

Crossrefs

Cf. A195111, A195110, A002260, A194959, A195107.

Programs

Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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