A131503 Nonnegative integers n for which cos(n) is positive.

0, 1, 5, 6, 7, 11, 12, 13, 14, 18, 19, 20, 24, 25, 26, 30, 31, 32, 37, 38, 39, 43, 44, 45, 49, 50, 51, 55, 56, 57, 58, 62, 63, 64, 68, 69, 70, 74, 75, 76, 81, 82, 83, 87, 88, 89, 93, 94, 95, 99, 100, 101, 102, 106, 107, 108, 112, 113, 114, 118, 119, 120, 125, 126, 127, 131, 132

Offset

1,3

Comments

Nonnegative integers n satisfying sin(n)<sec(n). - Clark Kimberling, Aug 26 2014

This is proved by taking sec(n)=1/cos(n), therefore considering sin(n)*cos(n)<1 for cos(n)>0 and sin(n)*cos(n)>1 for cos(n)<0. Since sin(n)*cos(n)=sin(2n)/2, the first case becomes sin(2n)<2 for cos(n)>0 which is always correct, and the second case becomes sin(2n)>2 for cos(n)<0 which is never correct. - R. J. Mathar, Sep 07 2014

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Cosine

Mathematica

Select[Range[150], Cos[#]>0&] (* Harvey P. Dale, Feb 02 2012 *)

Prog

(Sage) [i for i in range(200) if cos(i)>0] # Danny Rorabaugh, Mar 19 2015
(PARI) lista(nn) = for (n=0, nn, if (cos(n) > 0, print1(n, ", "))); \\ Michel Marcus, Mar 19 2015

Crossrefs

Sequence in context: A104122 A336857 A049467 * A047266 A026309 A073936

Adjacent sequences: A131500 A131501 A131502 * A131504 A131505 A131506

Keyword

easy,nonn

Author

Stephen Casey (hexomino(AT)gmail.com), Aug 13 2007

Extensions

0 inserted by R. J. Mathar, Sep 06 2014

Status

approved