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.

A194914 Fractalization of (1+[n/sqrt(8)]), 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/sqrt(8)]) is A194990.

Crossrefs

Cf. A194959, A194914, A194915, A194916.

Programs

  • Mathematica
    r = Sqrt[8]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194990  *)
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] (* A194914 *)
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}]]  (* A194915 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194916 *)

A194915 Interspersion fractally induced by A194990, 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, A194915 is a permutation of the positive integers, with inverse A194916.

Examples

			Northwest corner:
1...3...6...10..15..21
2...4...7...11..16..22
5...9...14..20..27..35
8...13..19..26..34..43
12..17..23..30..38..47

Crossrefs

Cf. A194959, A194990, A194915, A194916.

Programs

  • Mathematica
    r = Sqrt[8]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194990  *)
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] (* A194914 *)
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}]]  (* A194915 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194916 *)

A195078 Inverse permutation of A195077; every positive integer occurs exactly once.

Original entry on oeis.org

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, 36, 35, 34, 32, 31, 29, 38, 41, 44, 45, 43, 42, 40, 39, 37, 47, 50, 53, 55, 54, 52, 51, 49, 48, 46, 57, 60, 63, 66, 65, 64, 62, 61, 59, 58, 56, 68, 71, 74
Offset: 1

Views

Author

Clark Kimberling, Sep 08 2011

Keywords

Comments

Not the same as A194916.

Crossrefs

Cf. A195077, A195076.

Programs

Showing 1-3 of 3 results.

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