A000480 -id:A000480 - cp's OEIS frontend

A000503 a(n) = floor(tan(n)).

0, 1, -3, -1, 1, -4, -1, 0, -7, -1, 0, -226, -1, 0, 7, -1, 0, 3, -2, 0, 2, -2, 0, 1, -3, -1, 1, -4, -1, 0, -7, -1, 0, -76, -1, 0, 7, -1, 0, 3, -2, 0, 2, -2, 0, 1, -3, -1, 1, -4, -1, 0, -7, -1, 0, -46, -1, 0, 8, -1, 0, 3, -2, 0, 2, -2, 0, 1, -3, -1, 1, -4, -1, 0, -6, -1, 0, -33, -1, 0, 9, -1, 0, 3, -2, 0, 2, -2, 0, 1, -2, -1, 1, -3, -1, 0, -6, -1, 0, -26

Offset: 0

N. J. A. Sloane

Every integer appears infinitely often. - Charles R Greathouse IV, Aug 06 2012

Does not satisfy Benford's law [Whyman et al., 2016]. - N. J. A. Sloane, Feb 12 2017

T. D. Noe, Table of n, a(n) for n = 0..1000
David P. Bellamy, Jeffrey C. Lagarias, Felix Lazebnik, Proposed Problem: Large Values of Tan n
David P. Bellamy, Jeffrey C. Lagarias, Felix Lazebnik and Stephen M. Gagola, Jr., Large Values of Tangent: 10656, The American Mathematical Monthly, Vol. 106, No. 8 (Oct., 1999), pp. 782-784.
Daniel Forgues and Jon E. Schoenfield, Discussion of A000503
G. Whyman, N. Ohtori, E. Shulzinger, Ed. Bormashenko, Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?, Physica A: Statistical Mechanics and its Applications, 461 (2016), 595-601.
Index entries for sequences related to Benford's law

Cf. A005657, A000493, A000480, A000494, A000484, A088306, A195911, A195910, A037448, A258024.

[Floor(Tan(n)): n in [0..80]]; // Vincenzo Librandi, Jun 13 2015

Maple
```
f := n->floor(evalf(tan(n)));
```

Table[Floor[Tan[n]], {n, 0, 100}] (* Stefan Steinerberger, Apr 09 2006 *)

a(n)=tan(n)\1 \\ Charles R Greathouse IV, Sep 04 2014

More terms from Stefan Steinerberger, Apr 09 2006

A000493 a(n) = floor(sin(n)).

Original entry on oeis.org

0, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0

Offset: 0

N. J. A. Sloane

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A032615, A126564 (even bisection), A000480 (floor cos(n)).

[Floor(Sin(n)): n in [0..100]]; // Vincenzo Librandi, Jun 15 2015

Maple
```
f := n->floor(evalf(sin(n)));
```

f[ n_ ] := Floor[ N[ Sin[ n ] ] ]
Floor[Sin[Range[0,90]]] (* Harvey P. Dale, Dec 04 2012 *)

a(n) = -(A032615(n) mod 2). - Robert Israel, Jun 14 2015

A037448 a(n) = floor(cot(n)).

Original entry on oeis.org

0, -1, -8, 0, -1, -4, 1, -1, -3, 1, -1, -2, 2, 0, -2, 3, 0, -1, 6, 0, -1, 112, 0, -1, -8, 0, -1, -4, 1, -1, -3, 1, -1, -2, 2, 0, -2, 3, 0, -1, 6, 0, -1, 56, 0, -1, -9, 0, -1, -4, 1, -1, -3, 1, -1, -2, 2, 0, -2, 3, 0, -1, 5, 0, -1, 37, 0, -1, -9, 0, -1, -4, 1, -1, -3, 1, -1, -2, 2, 0, -2, 3, 0, -1, 5, 0, -1, 28, 0, -1, -10, 0, -1, -4, 1, -1, -3

Offset: 1

Jason Earls, Jun 30 2001

sign

Contains all integers infinitely often. - Charles R Greathouse IV, Aug 06 2012

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A195911, A195910, A000503, A005657, A000493, A000480, A000494, A000484.

[Floor(Cot(n)): n in [1..100]]; // Vincenzo Librandi, Jun 15 2015

Floor[Cot[Range[100]]] (* Harvey P. Dale, Dec 26 2024 *)

v=[]; for(n=1,260,v=concat(v,floor(cotan(n)))); v

a(44) corrected by T. D. Noe, Jan 21 2008

A126564 a(n) = floor( sin(n)*cos(n) ).

Original entry on oeis.org

0, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0

Offset: 0

Rick L. Shepherd, Dec 27 2006

sign

Cf. A000480, A000493, A126565.

PARI
```
a(n) = floor(sin(n)*cos(n))
```

a(n) = floor(sin(n)*cos(n)).

a(n) = floor(sin(2n)/2). [Wesley Ivan Hurt, Jun 22 2013]

A195911 a(n) = ceiling(cot(n)).

Original entry on oeis.org

1, 0, -7, 1, 0, -3, 2, 0, -2, 2, 0, -1, 3, 1, -1, 4, 1, 0, 7, 1, 0, 113, 1, 0, -7, 1, 0, -3, 2, 0, -2, 2, 0, -1, 3, 1, -1, 4, 1, 0, 7, 1, 0, 57, 1, 0, -8, 1, 0, -3, 2, 0, -2, 2, 0, -1, 3, 1, -1, 4, 1, 0, 6, 1, 0, 38, 1, 0, -8, 1, 0, -3, 2, 0, -2, 2, 0, -1, 3

Offset: 1

Mohammad K. Azarian, Mar 15 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A195910, A000503, A037448, A005657, A000493, A000480, A000494, A000484.

[Ceiling(1/Tan(n)): n in [1..80]]; // Vincenzo Librandi, Feb 16 2013

Table[Ceiling[Cot[n]], {n, 100}] (* T. D. Noe, Mar 16 2012 *)

a(n)=ceil(1/tan(n)) \\ Charles R Greathouse IV, Feb 07 2013

A249988 Integer part of sine of n degrees multiplied by 1000.

Original entry on oeis.org

0, 17, 34, 52, 69, 87, 104, 121, 139, 156, 173, 190, 207, 224, 241, 258, 275, 292, 309, 325, 342, 358, 374, 390, 406, 422, 438, 453, 469, 484, 500, 515, 529, 544, 559, 573, 587, 601, 615, 629, 642, 656, 669, 681, 694, 707, 719, 731, 743, 754, 766, 777, 788, 798, 809, 819, 829, 838, 848, 857, 866

Offset: 0

Alex Ratushnyak, Nov 11 2014

nonn

Due to multiplication by 1000 almost all a(n) are different for n<90, the only exception is a(89)=a(88)=999.

			sin(Pi/2) = sin(90 deg.) = 1, so a(90)=1000.

Cf. A000493, A000494, A000484, A000480, A249989.

Table[IntegerPart[1000*Sin[n Degree]],{n,0,60}] (* Harvey P. Dale, May 22 2015 *)

import math
for n in range(381): print(int(1000*math.sin(math.pi*n/180)), end=', ')

a(n) = round(1000*sin(Pi*n/180)), where round() is the rounding towards zero function.
a(360+n) = a(n).
a(180+n) = -a(n).

Corrected and extended by Harvey P. Dale, May 22 2015

cp's OEIS Frontend

A000503 a(n) = floor(tan(n)).

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A000493 a(n) = floor(sin(n)).

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A037448 a(n) = floor(cot(n)).

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A126564 a(n) = floor( sin(n)*cos(n) ).

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A195911 a(n) = ceiling(cot(n)).

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A249988 Integer part of sine of n degrees multiplied by 1000.

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