A195910 -id:A195910 - 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

A293751 Values of positive integer i such that floor(tan(-i)) = 1.

Original entry on oeis.org

18, 21, 40, 43, 62, 65, 84, 87, 90, 106, 109, 112, 128, 131, 134, 150, 153, 156, 172, 175, 178, 197, 200, 219, 222, 241, 244, 263, 266, 285, 288, 307, 310, 329, 332, 351, 354, 373, 376, 395, 398, 417, 420, 439, 442, 445, 461, 464, 467, 483, 486, 489, 505, 508, 511, 527, 530, 533, 552, 555, 574, 577, 596

Offset: 1

V.J. Pohjola, Oct 15 2017

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..1040

Cf. A000530, A293698, A293699, A293702, A293705, A293700, A293701, A293704. a(n) are also the roots of A195910(i)=1, starting from i=1.

rootsn = Flatten[Position[Table[Floor[Tan[-i]], {i, 1, 10^3}], 1]];
(*a(n) = rootsn[[n]]*)
Select[Range@600, Floor@Tan@-# == 1 &] (* Robert G. Wilson v, Nov 19 2017 *)

isok(n) = floor(tan(-n)) == 1; \\ Michel Marcus, Nov 03 2017

floor(tan(-n)) = -ceiling(tan(n)).

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

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

A005699 a(n) = ceiling(tan(n)^2).

Original entry on oeis.org

0, 3, 5, 1, 2, 12, 1, 1, 47, 1, 1, 51054, 1, 1, 53, 1, 1, 13, 2, 1, 6, 3, 1, 3, 5, 1, 2, 11, 1, 1, 42, 1, 1, 5673, 1, 1, 61, 1, 1, 14, 2, 1, 6, 3, 1, 3, 5, 1, 2, 11, 1, 1, 37, 1, 1, 2042, 1, 1, 70, 1, 1, 15, 2, 1, 6, 3, 1, 3, 5, 1, 2, 10, 1, 1, 33, 1, 1, 1042, 1, 1, 82, 1, 1, 16, 2, 1, 6, 3, 1, 3, 4, 1, 2, 9, 1, 1, 30, 1, 1, 630, 1, 1, 96, 1, 1, 17

Offset: 0

N. J. A. Sloane

For n > 0, a(n) = floor(sec(n)^2). - N. J. A. Sloane, Mar 17 2025

Cf. A005657, A195910.

a(n) = ceil(tan(n)^2); \\ Seiichi Manyama, Feb 28 2024

More terms from Seiichi Manyama, Feb 28 2024

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

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A293751 Values of positive integer i such that floor(tan(-i)) = 1.

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

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

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A005699 a(n) = ceiling(tan(n)^2).

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