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

Author

Clark Kimberling

Keywords

• nonn
• nice

Comments

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

Examples

			After the 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...
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..1000 (first 166 terms from Robert G. Wilson v)
• Carlos Hernan Lopez Zapata and Nikos Mantzakouras, Diophantine Flint-Hills series: convergence, polylogarithms and pi's bound, ResearchGate (2025). See pp. 16, 69.
• Eric Weisstein's World of Mathematics, Flint Hills Series
• Eric Weisstein's World of Mathematics, Secant

Crossrefs

Cf. A046947, A046956, A002485, A024814.

See also A382815.

Programs

Mathematica

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

PARI

e=2;for(n=0,1e9,abs(cos(n))M. F. Hasler, Apr 01 2013

Extensions

More terms from Olivier Gérard

Edited by Robert G. Wilson v, Jan 28 2003