A246413 - OEIS

%I #8 Jul 27 2020 20:06:33

%S 1,3,5,7,9,11,13,15,17,19,21,24,26,28,30,32,34,36,38,40,42,44,45,47,

%T 49,51,53,55,57,59,61,63,65,68,70,72,74,76,78,80,82,84,86,88,89,91,93,

%U 95,97,99,101,103,105,107,109,112,114,116,118,120,122,124,126

%N Positive integers k satisfying csc(k) > csc(k+1).

%C a(n), A246414, and A246415 partition the positive integers.

%H Clark Kimberling, <a href="/A246413/b246413.txt">Table of n, a(n) for n = 1..1000</a>

%t z = 200;

%t f[x_] := f[x] = Csc[x];

%t Select[Range[1, z], f[#] > f[# + 1] &]  (*A246413*)

%t Select[Range[1, z], f[#] < f[# + 1] > f[# + 2] &]  (*A246414 *)

%t Select[Range[1, z], f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (*A246415*)

%t Position[Partition[Csc[Range[130]],2,1],_?(#[[1]]>#[[2]]&),1,Heads-> False]// Flatten (* _Harvey P. Dale_, Jul 27 2020 *)

%Y Cf. A246414, A246415, A246410 (complement of a(n)).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Aug 25 2014