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 1-2 of 2 results.

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

Views

Author

Clark Kimberling, Sep 08 2011

Keywords

Comments

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.

Crossrefs

Cf. A195076, A195077, A195078.

Programs

  • Mathematica
    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 *)

A195077 Interspersion fractally induced by A009620, a rectangular array, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 10, 7, 9, 8, 15, 11, 14, 13, 12, 21, 16, 20, 19, 17, 18, 28, 22, 27, 26, 23, 25, 24, 36, 29, 35, 34, 30, 33, 32, 31, 45, 37, 44, 43, 38, 42, 41, 39, 40, 55, 46, 54, 53, 47, 52, 51, 48, 50, 49, 66, 56, 65, 64, 57, 63, 62, 58, 61, 60, 59, 78, 67, 77
Offset: 1

Views

Author

Clark Kimberling, Sep 08 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, A194977 is a permutation of the positive integers, with inverse A195078. A195077 is not A194915.

Crossrefs

Cf. A194959, A009620, A195076, A195078.

Programs

  • Mathematica
    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 *)
Showing 1-2 of 2 results.

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