OFFSET
1,2
COMMENTS
Conjecture: 2*k/Pi is either a little more than an even integer or a little less than an odd integer.
The conjecture is true. As k > 0 increases, satisfaction of the inequality k < sec(k)*csc(k) requires that sec(k)*csc(k) be a large positive number. Since sec(k)*csc(k) = 1/(sin(k)*cos(k)) = 2/sin(2*k), this requires that sin(2*k) be a small positive number, which occurs only when 2*k/Pi is a little more than an even integer or a little less than an odd integer. - Jon E. Schoenfield, Mar 06 2021
LINKS
Jon E. Schoenfield, Magma program
MATHEMATICA
Select[Range[10^6], # < Sec[#] Csc[#] &] (* Michael De Vlieger, Mar 14 2021 *)
PROG
(Python)
import math
i = 1;
while True:
if(i < 1/(math.cos(i)*math.sin(i))):
print(str(i) + ", ")
i += 1
(PARI) isok(k) = k < 1/(sin(k)*cos(k)); \\ Michel Marcus, Mar 05 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
José Mauricio de Oliveira Neto, Mar 04 2021
EXTENSIONS
a(22)-a(27) from Jon E. Schoenfield, Mar 06 2021
STATUS
approved