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.

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A194965 Fractalization of (A053824(n+5)), n>=0.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 6, 2, 3, 4, 5, 1, 6, 7, 2, 3, 4, 5, 1, 6, 7, 8, 2, 3, 4, 5, 1, 6, 7, 8, 9, 2, 3, 4, 5, 1, 6, 7, 8, 9, 10, 2, 3, 4, 5, 1, 6, 11, 7, 8, 9, 10, 2, 3, 4, 5, 1, 6, 11, 12, 7, 8, 9, 10, 2, 3, 4, 5, 1, 6, 11, 12, 13, 7, 8, 9, 10, 2, 3, 4, 5, 1, 6, 11
Offset: 1

Views

Author

Clark Kimberling, Sep 07 2011

Keywords

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (A053724(n+5)), n>=0 is formed by concatenating 5-tuples of the form (n,n+1,n+2, n+3,n+4) for n>=1: 1,2,3,4,5,2,3,4,5,6,3,4,5,6,7,...

Crossrefs

Cf. A194959, A194965, A194966, A194967.

Programs

  • Mathematica
    p[n_] := Floor[(n + 4)/5] + Mod[n - 1, 5]
Table[p[n], {n, 1, 90}]  (* A053824(n+5), n>=0 *)
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]   (* A194965 *)
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}]]  (* A194966 *)
q[n_] := Position[w, n]; Flatten[
Table[q[n], {n, 1, 80}]]  (* A194967 *)

A194967 Inverse permutation of A194966; every positive integer occurs exactly once.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 21, 17, 18, 19, 20, 22, 27, 28, 23, 24, 25, 26, 29, 34, 35, 36, 30, 31, 32, 33, 37, 42, 43, 44, 45, 38, 39, 40, 41, 46, 51, 52, 53, 54, 55, 47, 48, 49, 50, 56, 61, 66, 62, 63, 64, 65, 57, 58, 59, 60, 67, 72, 77
Offset: 1

Views

Author

Clark Kimberling, Sep 07 2011

Keywords

Links

Crossrefs

Cf. A194959, A194966 (inverse).

Programs

A194968 Fractalization of (1+[n/r]), where [ ]=floor, r=(1+sqrt(5))/2 (the golden ratio), and n>=1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 1, 3, 4, 2, 1, 3, 4, 5, 2, 1, 3, 4, 6, 5, 2, 1, 3, 4, 6, 7, 5, 2, 1, 3, 4, 6, 8, 7, 5, 2, 1, 3, 4, 6, 8, 9, 7, 5, 2, 1, 3, 4, 6, 8, 9, 10, 7, 5, 2, 1, 3, 4, 6, 8, 9, 11, 10, 7, 5, 2, 1, 3, 4, 6, 8, 9, 11, 12, 10, 7, 5, 2, 1, 3, 4, 6, 8, 9, 11, 12, 13, 10, 7, 5, 2, 1, 3, 4
Offset: 1

Views

Author

Clark Kimberling, Sep 07 2011

Keywords

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (1+[n/r]) is A019446.

Crossrefs

Cf. A194959, A019446, A194969, A194970.

Programs

  • Mathematica
    r = GoldenRatio; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A019446 *)
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]  (* A194968 *)
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}]]  (* A194969 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194970 *)

A194970 Inverse permutation of A194969; every positive integer occurs exactly once.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 7, 9, 10, 8, 11, 13, 14, 15, 12, 16, 18, 19, 21, 20, 17, 22, 24, 25, 27, 28, 26, 23, 29, 31, 32, 34, 36, 35, 33, 30, 37, 39, 40, 42, 44, 45, 43, 41, 38, 46, 48, 49, 51, 53, 54, 55, 52, 50, 47, 56, 58, 59, 61, 63, 64, 66, 65, 62, 60, 57, 67, 69, 70
Offset: 1

Views

Author

Clark Kimberling, Sep 07 2011

Keywords

Links

Crossrefs

Cf. A194969 (inverse), A194959.

Programs

A194973 Fractalization of (A053737(n+4)), n>=0.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 5, 2, 3, 4, 1, 5, 6, 2, 3, 4, 1, 5, 6, 7, 2, 3, 4, 1, 5, 6, 7, 8, 2, 3, 4, 1, 5, 9, 6, 7, 8, 2, 3, 4, 1, 5, 9, 10, 6, 7, 8, 2, 3, 4, 1, 5, 9, 10, 11, 6, 7, 8, 2, 3, 4, 1, 5, 9, 10, 11, 12, 6, 7, 8, 2, 3, 4, 1, 5, 9, 13, 10, 11, 12, 6, 7, 8, 2, 3, 4, 1, 5, 9
Offset: 1

Views

Author

Clark Kimberling, Sep 07 2011

Keywords

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (A053737(n+4)), n>=0 is formed by concatenating 4-tuples of the form (n,n+1,n+2, n+3) for n>=1: 1,2,3,4,2,3,4,5,3,4,5,6,...

Crossrefs

Cf. A194959, A194974, A194975.

Programs

  • Mathematica
    p[n_] := Floor[(n + 3)/4] + Mod[n - 1, 4]
Table[p[n], {n, 1, 90}]  (* A053737(n+4), n>=0 *)
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]  (* A194973 *)
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}]]  (* A194974 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194975 *)

A194975 Inverse permutation of A194974; every positive integer occurs exactly once.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 12, 13, 14, 16, 20, 21, 17, 18, 19, 22, 26, 27, 28, 23, 24, 25, 29, 33, 34, 35, 36, 30, 31, 32, 37, 41, 45, 42, 43, 44, 38, 39, 40, 46, 50, 54, 55, 51, 52, 53, 47, 48, 49, 56, 60, 64, 65, 66, 61, 62, 63, 57, 58, 59, 67, 71, 75
Offset: 1

Views

Author

Clark Kimberling, Sep 07 2011

Keywords

Comments

See A194959 and A194974.

Crossrefs

Cf. A194974.

Programs

A194978 Inverse permutation of A194977; every positive integer occurs exactly once.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 14, 15, 13, 16, 17, 19, 20, 21, 18, 22, 23, 25, 26, 28, 27, 24, 29, 30, 32, 33, 35, 36, 34, 31, 37, 38, 40, 41, 43, 44, 45, 42, 39, 46, 47, 49, 50, 52, 53, 54, 55, 51, 48, 56, 57, 59, 60, 62, 63, 64, 66, 65, 61, 58, 67, 68, 70
Offset: 1

Views

Author

Clark Kimberling, Sep 07 2011

Keywords

Crossrefs

Cf. A194977, A194976, A194959.

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 *)

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 *)

A195079 Fractalization of (1+[n/4]), where [ ]=floor.

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 3, 4, 2, 1, 3, 5, 4, 2, 1, 3, 6, 5, 4, 2, 1, 3, 7, 6, 5, 4, 2, 1, 3, 7, 8, 6, 5, 4, 2, 1, 3, 7, 9, 8, 6, 5, 4, 2, 1, 3, 7, 10, 9, 8, 6, 5, 4, 2, 1, 3, 7, 11, 10, 9, 8, 6, 5, 4, 2, 1, 3, 7, 11, 12, 10, 9, 8, 6, 5, 4, 2, 1, 3, 7, 11, 13, 12, 10, 9, 8, 6, 5, 4, 2, 1, 3, 7, 11
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/4]) is A008621. See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.

Crossrefs

Cf. A008621, A195080, A195081.

Programs

  • Mathematica
    r = 4; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A008621 *)
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] (* A195079 *)
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}]] (* A195080 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195081 *)
Previous Showing 31-40 of 61 results. Next

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