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.

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

A195110 Fractalization of the fractal sequence A002260. Interspersion fractally induced by A002260.

Original entry on oeis.org

1, 2, 1, 2, 3, 1, 4, 2, 3, 1, 4, 5, 2, 3, 1, 4, 5, 6, 2, 3, 1, 7, 4, 5, 6, 2, 3, 1, 7, 8, 4, 5, 6, 2, 3, 1, 7, 8, 9, 4, 5, 6, 2, 3, 1, 7, 8, 9, 10, 4, 5, 6, 2, 3, 1, 11, 7, 8, 9, 10, 4, 5, 6, 2, 3, 1, 11, 12, 7, 8, 9, 10, 4, 5, 6, 2, 3, 1, 11, 12, 13, 7, 8, 9, 10, 4, 5, 6, 2, 3, 1, 11, 12
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. The sequence A002260 is the fractal sequence obtained by concatenating the segments 1; 12; 123; 1234; 12345;...

Crossrefs

Cf. A194959, A002260, A195111, 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 *)

A195114 Interspersion fractally induced by the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 10, 7, 8, 9, 15, 12, 13, 14, 11, 21, 18, 19, 20, 16, 17, 28, 25, 26, 27, 22, 23, 24, 36, 33, 34, 35, 29, 30, 31, 32, 45, 42, 43, 44, 38, 39, 40, 41, 37, 55, 52, 53, 54, 48, 49, 50, 51, 46, 47, 66, 63, 64, 65, 59, 60, 61, 62, 56, 57, 58, 78, 75, 76
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, A194114 is a permutation of the positive integers, with inverse A195115.

Examples

			Northwest corner:
1...3...6...10..15..21..28
2...4...7...12..18..25..33
5...8...13..19..26..34..43
9...14..20..27..35..44..54
11..16..22..29..38..48..59

Crossrefs

Cf. A194959, A002260, A195113, A195115, A195111.

Programs

  • Mathematica
    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 *)
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.