A337249 - OEIS

%I #43 Apr 11 2023 10:18:52

%S 1,3,44,710,1420,2130,2840,312689,10838702,6167950454,21053343141,

%T 63160029423,105266715705

%N Numbers k for which csc(k) > k.

%C a(14) > 1.129*10^12, if it exists. - _Kevin P. Thompson_, Nov 07 2021

%C 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

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

%t Select[Range[10^6], Csc[#] > # &] (* _Amiram Eldar_, Aug 21 2020 *)

%o (Python)

%o import math

%o i = 1

%o while True:

%o   if 1 / math.sin(i) > i:

%o     print(i)

%o   i += 1

%o (PARI) isok(m) = 1/sin(m) > m; \\ _Michel Marcus_, Aug 27 2020

%Y Subsequence of A080142, A046955.

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

%Y Cf. A092328, A337248.

%K nonn,more

%O 1,2

%A _Joseph C. Y. Wong_, Aug 21 2020

%E a(11)-a(13) from _Kevin P. Thompson_, Nov 07 2021