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

1,2

Comments

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

Links

Jwalin Bhatt, Table of n, a(n) for n = 1..997

Example

cos(411557987) = 0.999999999999999996782535835854909099962858791940...

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 *)

Prog

(Python)
from sympy import pi, continued_fraction_iterator, continued_fraction_convergents
from itertools import islice
A046955 = [1] + [f.numerator for f in list(continued_fraction_convergents(islice(continued_fraction_iterator(2*pi), 20)))]  # Jwalin Bhatt, Dec 30 2025

Crossrefs

Cf. A046947.

Cf. A242859 (denominators).

Sequence in context: A294313 A383541 A235537 * A042215 A041911 A372302

Adjacent sequences: A046952 A046953 A046954 * A046956 A046957 A046958

Keyword

nonn,frac

Author

Olivier Gérard

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.

Status

approved