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 1-5 of 5 results.

A109234 a(n) = floor(n*sinh(1)).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Comments

Beatty sequence for sinh(1) = (e-1/e)/2 = 1.17520... = A073742; complement of A109235.

Links

Crossrefs

Cf. A109236, A109231, A109237.

A109239 Self-inverse integer permutation induced by Beatty sequences for (e^2+1)/(e^2-1) and (e^2+1)/2.

Original entry on oeis.org

4, 8, 12, 1, 16, 20, 25, 2, 29, 33, 37, 3, 41, 46, 50, 5, 54, 58, 62, 6, 67, 71, 75, 79, 7, 83, 88, 92, 9, 96, 100, 104, 10, 109, 113, 117, 11, 121, 125, 130, 13, 134, 138, 142, 146, 14, 151, 155, 159, 15, 163, 167, 171, 17, 176, 180, 184, 18, 188, 192
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Comments

a(n) = A164088(n) for n <= 26. [Reinhard Zumkeller, Aug 11 2009]

Links

Crossrefs

Cf. A109233, A109236, A109237, A109238.

Formula

a(A109237(n))=A109238(n) and a(A109238(n))=A109237(n).

A109231 a(n) = floor(n*cosh(1)).

Original entry on oeis.org

1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 91, 92, 94, 95, 97, 98, 100
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Comments

Beatty sequence for cosh(1) = (e+1/e)/2 = 1.54308...= A073743; complement of A109232.

Links

Crossrefs

Cf. A073743, A109232, A109233, A109234, A109237, A059563.

A109238 a(n) = floor(n*(e^2+1)/2).

Original entry on oeis.org

4, 8, 12, 16, 20, 25, 29, 33, 37, 41, 46, 50, 54, 58, 62, 67, 71, 75, 79, 83, 88, 92, 96, 100, 104, 109, 113, 117, 121, 125, 130, 134, 138, 142, 146, 151, 155, 159, 163, 167, 171, 176, 180, 184, 188, 192, 197, 201, 205, 209, 213, 218, 222, 226
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Comments

Beatty sequence for (e^2+1)/2 = 4.19452...; complement of A109237.
From Reinhard Zumkeller, Aug 11 2009: (Start)
a(n) = A164086(n) for n <= 66;
a(n) = A109239(A109237(n)) and A109239(a(n)) = A109237(n). (End)

Links

Crossrefs

Cf. A109237, A109239, A164086.

Programs

  • Mathematica
    Floor[Range[60] (E^2+1)/2] (* Harvey P. Dale, Apr 10 2018 *)

Extensions

Typo in comment corrected by Reinhard Zumkeller, Aug 10 2009

A164087 Beatty sequence for 4*Pi/(4*Pi-3) = 1.3135986... .

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 89, 90, 91, 93, 94
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 11 2009

Keywords

Comments

a(n) = A109237(n) for n <= 66;
complement of A164086;
a(n) = A164088(A164086(n)) and A164088(a(n)) = A164086(n).

Links

Crossrefs

Cf. A109237, A164086, A164088.

Programs

  • Mathematica
    Floor[4 Range[100]*Pi/(4*Pi - 3)] (* Wesley Ivan Hurt, Apr 25 2023 *)

Formula

a(n) = floor(4*n*Pi/(4*Pi-3)).
Showing 1-5 of 5 results.

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