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.
%I A327138 #16 Oct 21 2024 15:52:17 %S A327138 2,5,8,11,12,14,15,17,18,20,21,24,27,30,33,34,36,37,39,40,42,43,46,49, %T A327138 52,55,56,58,59,61,62,64,65,68,71,74,77,78,80,81,83,84,86,87,90,93,96, %U A327138 99,100,102,103,105,106,108,109,112,115,118,121,122,124,125 %N A327138 Numbers k such that cos(2k) < cos(2k+2). %C A327138 The sequences A327138, A327139, A327140 partition the positive integers. %C A327138 Conjecture: 2.07 < n*Pi - a(n) < 3.08 for n >= 1. %H A327138 Clark Kimberling, <a href="/A327138/b327138.txt">Table of n, a(n) for n = 1..10000</a> %e A327138 (cos 2, cos 4, ...) = (-0.4, -0.6, 0.9, -0.1, -0.8, ...) approximately, so that the differences, in sign, are - + - - + - - + - - + +, with "+" in places 2,5,8,11,12,... (A327138), "- +" starting in places 1,4,7,10,13,... (A327139), and "- - +" starting in places 3,6,9,22,25,... (A327140). %t A327138 z = 500; f[x_] := f[x] = Cos[2 x]; t = Range[1, z]; %t A327138 Select[t, f[#] < f[# + 1] &] (* A327138 *) %t A327138 Select[t, f[#] > f[# + 1] < f[# + 2] &] (* A327139 *) %t A327138 Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &] (* A327140 *) %t A327138 Position[Partition[Cos[2Range[200]],2,1],_?(#[[1]]<#[[2]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Oct 21 2024 *) %Y A327138 Cf. A026309, A246303, A026317, A327139. %K A327138 nonn,easy %O A327138 1,1 %A A327138 _Clark Kimberling_, Aug 23 2019