A337249 Numbers k for which csc(k) > k.

1, 3, 44, 710, 1420, 2130, 2840, 312689, 10838702, 6167950454, 21053343141, 63160029423, 105266715705

Offset

1,2

Comments

a(14) > 1.129*10^12, if it exists. - Kevin P. Thompson, Nov 07 2021

a(14) exists. The numbers 428224593349304, 6134899525417045, 66627445592888887, 430010946591069243, and 2646693125139304345 all satisfy csc(k) > k and are larger than a(13). It is not yet proven whether these are a(14) - a(18) or if there are any other numbers in the sequence before or between them. - Wolfe Padawer, Apr 11 2023

Links

Table of n, a(n) for n=1..13.

Example

csc(1) = 1.1884... so 1 is a term.

Mathematica

Select[Range[10^6], Csc[#] > # &] (* Amiram Eldar, Aug 21 2020 *)

Prog

(Python)
import math
i = 1
while True:
  if 1 / math.sin(i) > i:
    print(i)
  i += 1
(PARI) isok(m) = 1/sin(m) > m; \\ Michel Marcus, Aug 27 2020

Crossrefs

Subsequence of A080142, A046955.

Subsequence of A265735 and A325158 if you omit the first term of A337249.

Cf. A092328, A337248.

Sequence in context: A353878 A359631 A011916 * A259785 A369944 A193623

Adjacent sequences: A337246 A337247 A337248 * A337250 A337251 A337252

Keyword

nonn,more

Author

Joseph C. Y. Wong, Aug 21 2020

Extensions

a(11)-a(13) from Kevin P. Thompson, Nov 07 2021

Status

approved