cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A342171 Nonnegative integers k such that k < sec(k)*csc(k).

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%I A342171 #46 Apr 23 2021 03:51:27
%S A342171 1,22,44,355,710,1065,1420,1775,2130,2485,2840,3195,260515,312689,
%T A342171 1146408,5419351,10838702,37362253,122925461,534483448,3083975227,
%U A342171 902209779836,74357078147863,214112296674652,642336890023956,18190586279576483,248319196091979065
%N A342171 Nonnegative integers k such that k < sec(k)*csc(k).
%C A342171 Conjecture: 2*k/Pi is either a little more than an even integer or a little less than an odd integer.
%C A342171 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
%H A342171 Jon E. Schoenfield, <a href="/A342171/a342171_1.txt">Magma program</a>
%t A342171 Select[Range[10^6], # < Sec[#] Csc[#] &] (* _Michael De Vlieger_, Mar 14 2021 *)
%o A342171 (Python)
%o A342171 import math
%o A342171 i = 1;
%o A342171 while True:
%o A342171   if(i < 1/(math.cos(i)*math.sin(i))):
%o A342171     print(str(i) + ", ")
%o A342171   i += 1
%o A342171 (PARI) isok(k) = k < 1/(sin(k)*cos(k)); \\ _Michel Marcus_, Mar 05 2021
%Y A342171 Cf. A249836, A332095, A337371.
%K A342171 nonn
%O A342171 1,2
%A A342171 _José Mauricio de Oliveira Neto_, Mar 04 2021
%E A342171 a(22)-a(27) from _Jon E. Schoenfield_, Mar 06 2021