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.

A347065 Rectangular array (T(n,k)), by antidiagonals: T(n,k) = position of k in the ordering of {h/r^m, r = (1+sqrt(5))/2, h >= 1, 0 <= m <= n}.

Original entry on oeis.org

1, 3, 1, 4, 3, 1, 6, 5, 3, 1, 8, 7, 5, 3, 1, 9, 9, 7, 5, 3, 1, 11, 11, 10, 7, 5, 3, 1, 12, 13, 12, 10, 7, 5, 3, 1, 14, 15, 14, 12, 10, 7, 5, 3, 1, 16, 17, 16, 15, 12, 10, 7, 5, 3, 1, 17, 19, 19, 17, 15, 12, 10, 7, 5, 3, 1, 19, 21, 21, 20, 17, 15, 12, 10, 7
Offset: 1

Views

Author

Clark Kimberling, Aug 16 2021

Keywords

Examples

			Corner:
   1 3 4 6  8  9 11 12 14 16 17 19 21
   1 3 5 7  9 11 13 15 17 19 21 23 25
   1 3 5 7 10 12 14 16 19 21 23 25 28
   1 3 5 7 10 12 15 17 20 22 24 26 29
   1 3 5 7 10 12 15 17 20 22 24 27 30
   1 3 5 7 10 12 15 17 20 22 24 27 30
   1 3 5 7 10 12 15 17 20 22 24 27 30

Crossrefs

Cf. A000201 (row 1), A005408 (row 2), A190511 (row 3), A020959 (limiting row).
Cf. A347066, A347067, A347068, A347069.

Programs

  • Mathematica
    z = 100; r = N[(1 + Sqrt[5])/2];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347065, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347065, sequence *)

A347066 Rectangular array (T(n,k)), by antidiagonals: T(n,k) is the position of k in the ordering of {h/r^m, r = sqrt(2), h >= 1, 0 <= m <= n}.

Original entry on oeis.org

1, 3, 1, 5, 3, 1, 6, 6, 3, 1, 8, 7, 7, 3, 1, 10, 10, 8, 7, 3, 1, 11, 12, 11, 8, 7, 3, 1, 13, 14, 14, 12, 8, 7, 3, 1, 15, 16, 16, 15, 12, 8, 7, 3, 1, 17, 19, 18, 17, 16, 12, 8, 7, 3, 1, 18, 21, 21, 19, 18, 16, 12, 8, 7, 3, 1, 20, 23, 23, 23, 20, 18, 16, 12, 8
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2021

Keywords

Examples

			Corner:
  1, 3, 5, 6,  8, 10, 11, 13, 15, 17, 18, 20, ...
  1, 3, 6, 7, 10, 12, 14, 16, 19, 21, 23, 25, ...
  1, 3, 7, 8, 11, 14, 16, 18, 21, 23, 25, 28, ...
  1, 3, 7, 8, 12, 15, 17, 19, 23, 25, 27, 30, ...
  1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
  1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
  1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
  ...

Crossrefs

Cf. A003152 (row 1), A347065, A347067, A347068, A347069.

Programs

  • Mathematica
    z = 100; r = N[Sqrt[2]];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347066, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347066, sequence *)

A347067 Rectangular array (T(n,k)), by antidiagonals: T(n,k) = position of k in the ordering of {h/r^m, r = 1/sqrt(2), h >= 1, 0 <= m <= n}.

Original entry on oeis.org

2, 4, 4, 7, 8, 6, 9, 13, 13, 10, 12, 17, 21, 21, 15, 14, 21, 28, 33, 32, 19, 16, 22, 34, 44, 49, 40, 25, 19, 26, 35, 54, 66, 61, 51, 41, 21, 30, 41, 55, 82, 82, 78, 83, 63, 24, 35, 48, 65, 83, 102, 105, 126, 128, 95, 26, 38, 56, 76, 98, 103, 130, 169, 193
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2021

Keywords

Examples

			Corner:
   2,  4,   7,   9,  12,  14,  16,  19,  21, ...
   4,  8,  13,  17,  21,  22,  26,  30,  35, ...
   6, 13,  21,  28,  34,  35,  41,  48,  56, ...
  10, 21,  33,  44,  54,  55,  65,  76,  88, ...
  15, 32,  49,  66,  82,  83,  98, 115, 133, ...
  19, 40,  61,  82, 102, 103, 122, 143, 165, ...
  25, 51,  78, 105, 130, 131, 156, 183, 210, ...
  41, 83, 126, 169, 210, 211, 252, 283, 310, ...
  ...

Crossrefs

Cf. A003151 (row 1), A347065, A347066, A347068, A347069.

Programs

  • Mathematica
    z = 100; r = N[1/Sqrt[2]];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347067, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347067, sequence *)

A347069 Rectangular array (T(n,k)), by downward antidiagonals: T(n,k) = position of k in the ordering of {h*e^m, h >= 1, 0 <= m <= n}.

Original entry on oeis.org

1, 2, 1, 4, 2, 1, 5, 4, 2, 1, 6, 5, 4, 2, 1, 8, 6, 5, 4, 2, 1, 9, 8, 6, 5, 4, 2, 1, 10, 9, 8, 6, 5, 4, 2, 1, 12, 11, 9, 8, 6, 5, 4, 2, 1, 13, 13, 11, 9, 8, 6, 5, 4, 2, 1, 15, 14, 13, 11, 9, 8, 6, 5, 4, 2, 1, 16, 16, 14, 13, 11, 9, 8, 6, 5, 4, 2, 1, 17, 17
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2021

Keywords

Comments

No two rows are identical.

Examples

			m = 0 gives 1, 2, 3, 4, 5, 6, ...
m = 1 gives e, 2e, 3e, 4e, 5e, ...
Row 1 of the array tells the positions of the positive integers when the numbers for m=0 and m=1 are jointly ranked.  Using decimal approximations, the numbers, jointly ranked, are 1, 2, 2.718, 3, 4, 5, 6.436, 6, 7, 8, 8.154, 9, 10, 10.873, 11, ...
Corner:
  1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18

Crossrefs

Cf. A347065, A347066, A347067, A347068.

Programs

  • Mathematica
    z = 100; r = N[E];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347069, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347069, sequence *)
Showing 1-4 of 4 results.

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