A004112 Numbers k where |cos(k)| (or |cosec(k)| or |cot(k)|) decreases monotonically to 0; also |tan(k)|, |sec(k)|, |sin(k)| increases.

0, 1, 2, 5, 8, 11, 344, 699, 1054, 1409, 1764, 2119, 2474, 2829, 3184, 3539, 3894, 4249, 4604, 4959, 5314, 5669, 6024, 6379, 6734, 7089, 7444, 7799, 8154, 8509, 8864, 9219, 9574, 9929, 10284, 10639, 10994, 11349, 11704, 12059, 12414, 12769, 13124, 13479, 13834

Offset

1,3

Comments

a(167) > 10^10. - Robert G. Wilson v, Nov 04 2019

a(100), a(1000), and a(10000) have 5, 215, and 221 digits, respectively. - Jon E. Schoenfield, Nov 08 2019

a(n) is also the smallest nonnegative integer k such that k mod Pi is closer to Pi/2 than any previous term. - Colin Linzer, Apr 27 2022

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..1000 (first 166 terms from Robert G. Wilson v)

Eric Weisstein's World of Mathematics, Flint Hills Series

Eric Weisstein's World of Mathematics, Secant

Example

After 151st term, the sequence continues 51819, 52174, 260515, 573204, 4846147, ...
|cos(4846147)| = 0.000000255689511369808141413171..., |cosec(4846147)| = 1.00000000000003268856311..., or |cot(4846147)| = 0.000000255689511369816499535901...
|tan(4846147)| = 3910993.43356970986068082..., |sec(4846147)| = 3910993.43356983770543651..., |sin(4846147)| = 0.999999999999967311436888...

Mathematica

a = -1; Do[b = N[ Abs[ Tan[n]], 24]; If[b > a, Print[n]; a = b], {n, 0, 13833}]

Prog

(PARI) e=2; for(n=0, 1e9, abs(cos(n))<e & !print1(n", ") & e=abs(cos(n))) \\ M. F. Hasler, Apr 01 2013

Crossrefs

Cf. A046947, A046956, A002485, A024814.

Sequence in context: A056661 A229883 A135050 * A024815 A073837 A357505

Adjacent sequences: A004109 A004110 A004111 * A004113 A004114 A004115

Keyword

nonn,nice

Author

Clark Kimberling

Extensions

More terms from Olivier Gérard

Edited by Robert G. Wilson v, Jan 28 2003

Status

approved