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 1-4 of 4 results.

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 *)

A194916 Inverse permutation of A194915; 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

Crossrefs

Cf. A194915, A194914, A194959.

Programs

A194990 a(n) = 1+ floor(n/sqrt(8)).

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27
Offset: 1

Views

Author

Clark Kimberling, Sep 08 2011

Keywords

Links

Crossrefs

Cf. A172474, A194914, A286655 (first differences).

Programs

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 *)
Showing 1-4 of 4 results.

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