A046955 Numbers k such that sec(k) decreases monotonically to 1 (or cos(k) increases to 1).

1, 6, 19, 25, 44, 333, 710, 103993, 312689, 1980127, 2292816, 4272943, 10838702, 80143857, 411557987, 2137933792, 2549491779, 12335900908, 14885392687, 42106686282, 1783366216531, 8958937768937, 279510437053578, 288469374822515, 567979811876093

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• frac

Comments

Also numerators of convergents to 2*Pi. - Vladeta Jovovic, Nov 09 2004

Examples

			cos(411557987) = 0.999999999999999996782535835854909099962858791940...
		

Crossrefs

Cf. A046947.

Cf. A242859 (denominators).

Programs

Mathematica

a = 0; Do[ If[ Cos[n] > a, Print[n]; a = Cos[n]], {n, 1, 421000000}] (* Robert G. Wilson v, Dec 29 2003 *)
b = 10; Do[ If[ Abs[ Mod[n + Pi/2, 2Pi] - Pi/2] < b, Print[n]; b = Abs[ Mod[n + Pi/2, 2Pi] - Pi/2]], {n, 1, 421000000}] (* Robert G. Wilson v, Dec 29 2003 *)
Join[{1}, Numerator[Convergents[2Pi, 33]]] (* Stéphane Mottelet, Oct 12 2011 *)

Extensions

More terms from Michel ten Voorde

One more term from Vladeta Jovovic, Apr 03 2000

8 more terms from Vladeta Jovovic, Nov 09 2004

More terms from Stéphane Mottelet, Oct 12 2011

Definition corrected by N. J. A. Sloane, Mar 16 2018 following a suggestion from Allan C. Wechsler.