A126564 -id:A126564 - cp's OEIS frontend

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

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

A126565 a(n) = ceiling(sin(n)*cos(n)).

Original entry on oeis.org

0, 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, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1

Offset: 0

Rick L. Shepherd, Dec 27 2006

nonn

For all nonzero integers n, ceiling(sin(n)*cos(n)) = 1 + floor(sin(n)*cos(n)), so a(n) = 1 + A126564(n) for n > 0 (a(0) = A126564(0) = 0).

Cf. A126564.

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

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

A181059 a(n) = floor(sin(n) - cos(n)).

Original entry on oeis.org

-1, 0, 1, 1, -1, -2, -2, -1, 1, 1, 0, -2, -2, -1, 0, 1, 0, -1, -2, -1, 0, 1, 0, -1, -2, -2, 0, 1, 1, 0, -2, -2, -1, 1, 1, 0, -1, -2, -1, 0, 1, 0, -1, -2, -1, 0, 1, 1, -1, -2, -2, -1, 1, 1, 0, -2, -2, -1, 0, 1, 0, -1, -2, -1, 0, 1, 0, -1, -2, -2, 0, 1, 1, 0, -2, -2, -1, 1, 1, 0, -1, -2, -1, 0

Offset: 0

Jonathan D. B. Hodgson, Oct 01 2010

G. C. Greubel, Table of n, a(n) for n = 0..500

Cf. A126564 (floor sin(n)*cos(n)).

[Floor(Sin(n) - Cos(n)): n in [0..120]]; // G. C. Greubel, Apr 05 2021

A181059 := proc(n) -sqrt(2)*cos(n+Pi/4) ; floor(%) ; end proc: seq(A181059(n), n=0..120) ; # R. J. Mathar, Oct 03 2010

Table[Floor[Sin[n]-Cos[n]],{n,0,120}] (* Harvey P. Dale, Jun 01 2018 *)

[floor(-sqrt(2)*cos(n+pi/4)) for n in (0..120)] # G. C. Greubel, Apr 05 2021

a(n) = floor( -sqrt(2)*cos(n + Pi/4) ). - R. J. Mathar, Oct 03 2010

More terms from R. J. Mathar, Oct 03 2010

A372456 a(n) = 1 if abs(tan(n)) > 1, 0 otherwise.

Original entry on oeis.org

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

Offset: 1

Ahmad J. Masad, May 01 2024

			For n = 43, tan(43) = -1.498387339..., and abs(-1.498387339...) > 1, so a(43) = 1.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A126565, A126564, A330035.

Table[Boole[Abs[Tan[n]] > 1], {n, 1, 100}] (* Amiram Eldar, May 02 2024 *)

a(n) = abs(tan(n)) > 1; \\ Michel Marcus, May 01 2024

cp's OEIS Frontend

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

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A126565 a(n) = ceiling(sin(n)*cos(n)).

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A181059 a(n) = floor(sin(n) - cos(n)).

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A372456 a(n) = 1 if abs(tan(n)) > 1, 0 otherwise.

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