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.

A194054 Natural interspersion of A054347; a rectangular array, by antidiagonals.

Original entry on oeis.org

1, 4, 2, 8, 5, 3, 14, 9, 6, 7, 22, 15, 10, 11, 12, 31, 23, 16, 17, 18, 13, 42, 32, 24, 25, 26, 19, 20, 54, 43, 33, 34, 35, 27, 28, 21, 68, 55, 44, 45, 46, 36, 37, 29, 30, 84, 69, 56, 57, 58, 47, 48, 38, 39, 40, 101, 85, 70, 71, 72, 59, 60, 49, 50, 51, 41, 120, 102
Offset: 1

Views

Author

Clark Kimberling, Aug 15 2011

Keywords

Comments

See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194054 is a permutation of the positive integers; its inverse is A194055.

Examples

			Northwest corner:
1...4...8...14...22...31
2...5...9...15...23...32
3...6...10..16...24...33
7...11..17..25...34...45

Crossrefs

Cf. A194029, A054347, A194053, A194058.

Programs

  • Mathematica
    z = 40; g = GoldenRatio
c[k_] := Sum[Floor[j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}]  (* A054347 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}]  (* A194053 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]]  (* A194054 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194058 *)

A194056 Natural interspersion of A000071(Fibonacci numbers minus 1), a rectangular array, by antidiagonals.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 11, 20, 21, 22, 23, 16, 17, 33, 34, 35, 36, 24, 25, 18, 54, 55, 56, 57, 37, 38, 26, 19, 88, 89, 90, 91, 58, 59, 39, 27, 28, 143, 144, 145, 146, 92, 93, 60, 40, 41, 29, 232, 233, 234, 235, 147, 148, 94, 61, 62, 42, 30
Offset: 1

Views

Author

Clark Kimberling, Aug 13 2011

Keywords

Comments

See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194056 is a permutation of the positive integers; its inverse is A194057.

Examples

			Northwest corner:
1...2...4...7...12
3...5...8...13..21
6...9...14..22..35
10..15..23..36..57
11..16..24..37..58

Crossrefs

Cf. A194029, A194055, A000071, A000045, A194057.

Programs

  • Mathematica
    z = 50;
c[k_] := -1 + Fibonacci[k + 2]
c = Table[c[k], {k, 1, z}] (* A000071, F(n+2)-1 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}]   (* A194055 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 11}, {k, 1, n}]] (* A194056 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194057 *)

A194059 Natural interspersion of A001911 (Fibonacci numbers minus 2); a rectangular array, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 11, 7, 8, 9, 19, 12, 13, 14, 10, 32, 20, 21, 22, 15, 16, 53, 33, 34, 35, 23, 24, 17, 87, 54, 55, 56, 36, 37, 25, 18, 142, 88, 89, 90, 57, 58, 38, 26, 27, 231, 143, 144, 145, 91, 92, 59, 39, 40, 28, 375, 232, 233, 234, 146, 147, 93, 60, 61, 41, 29
Offset: 1

Views

Author

Clark Kimberling, Aug 14 2011

Keywords

Comments

See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194059 is a permutation of the positive integers; its inverse is A194060.

Examples

			Northwest corner:
1...3...6...11...19
2...4...7...12...30
5...8...13..21...34
9...14..22..35...56
10..15..23..36...57

Crossrefs

Cf. A194029, A194059, A194062.

Programs

  • Mathematica
    z = 50;
c[k_] := -2 + Fibonacci[k + 3];
c = Table[c[k], {k, 1, z}]  (* A001911, F(n+3)-2 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 700}]   (* cf. A194055 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A194059 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 100}]] (* A194060 *)
Showing 1-3 of 3 results.

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