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.

A109237 a(n) = floor(n*coth(1)).

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
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Comments

Beatty sequence for coth(1) = (e^2+1)/(e^2-1) = 1.31303... = A073747; complement of A109238.
From Reinhard Zumkeller, Aug 11 2009: (Start)
a(n) = A164087(n) for n <= 20;
a(n) = A109239(A109238(n)) and A109239(a(n)) = A109238(n). (End)

Links

Crossrefs

Cf. A109238, A109239, A109231, A109234.
Cf. A073747.

Extensions

Typo in comment corrected by Reinhard Zumkeller, Aug 10 2009

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.

A109235 a(n) = floor(n*(e^2-1)/(e^2-2*e-1)).

Original entry on oeis.org

6, 13, 20, 26, 33, 40, 46, 53, 60, 67, 73, 80, 87, 93, 100, 107, 114, 120, 127, 134, 140, 147, 154, 160, 167, 174, 181, 187, 194, 201, 207, 214, 221, 228, 234, 241, 248, 254, 261, 268, 275, 281, 288, 295, 301, 308, 315, 321, 328, 335, 342, 348
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Comments

Beatty sequence for (e^2-1)/(e^2-2*e-1) = 6.70772...; complement of A109234.

Links

Crossrefs

Cf. A109234, A109236.

A109236 Self-inverse integer permutation induced by Beatty sequences for (e-1/e)/2 and (e^2+1)/(e^2-2*e-1).

Original entry on oeis.org

6, 13, 20, 26, 33, 1, 40, 46, 53, 60, 67, 73, 2, 80, 87, 93, 100, 107, 114, 3, 120, 127, 134, 140, 147, 4, 154, 160, 167, 174, 181, 187, 5, 194, 201, 207, 214, 221, 228, 7, 234, 241, 248, 254, 261, 8, 268, 275, 281, 288, 295, 301, 9, 308, 315
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2005

Keywords

Links

Crossrefs

Cf. A109233, A109234, A109235, A109239.

Formula

a(A109234(n))=A109235(n) and a(A109235(n))=A109234(n).

A335137 a(n) = floor(n*Im(2*e^(i*Pi/5))).

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, 67, 68, 69, 70, 71, 72
Offset: 1

Views

Author

Karl V. Keller, Jr., May 24 2020

Keywords

Comments

This is the Beatty sequence for imaginary part of 2*e^(i*Pi/5).
Im(2*e^(i*Pi/5)) = A182007 = 1.1755705045849462583374119... = 2*sin(Pi/5).
The real part of floor(n*2*e^(i*Pi/5)) is A000201 (floor(n*phi)).
Re(2*e^(i*Pi/5)) = A001622 = phi = (1 + sqrt(5))/2.
For n < 57, a(n) = A109234(n).

Examples

			For n = 3, floor(3*1.17557) = 3.

Links

Crossrefs

Cf. A000201, A001622, A109234, A182007.

Programs

  • Mathematica
    Array[Floor[# Im[2 E^(I*Pi/5)]] &, 62] (* Michael De Vlieger, May 24 2020 *)
  • Python
    from sympy import floor, im, exp, I, pi
for n in range(1, 101): print(floor(n*im(2*exp(I*pi/5))), end=', ')
Showing 1-5 of 5 results.

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