A026311 n-th nonnegative integer k satisfying cos(k) > cos(k+1).

0, 1, 2, 6, 7, 8, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 33, 34, 38, 39, 40, 44, 45, 46, 50, 51, 52, 57, 58, 59, 63, 64, 65, 69, 70, 71, 75, 76, 77, 78, 82, 83, 84, 88, 89, 90, 94, 95, 96, 101, 102, 103, 107, 108, 109, 113, 114, 115

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

The sequences A026311, A246300, A246301, A246302 partition the nonnegative integers.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A246293, A246300, A246301, A246302, A246303 (complement of A026311).

Programs

Mathematica

z = 520; f[x_] := f[x] = Cos[x]; t = Range[0, z];
Select[t, f[#] > f[# + 1] &]  (* A026311 *)
Select[t, f[#] < f[# + 1] > f[# + 2] &]  (* A246300 *)
Select[t, f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (* A246301 *)
Select[t, f[#] < f[# + 1] < f[# + 2] < f[# + 3] > f[# + 4] &] (* A246302 *)
Join[{0},Position[Partition[Cos[Range[120]],2,1],?(#[[1]]>#[[2]]&),1,Heads -> False]//Flatten] (* _Harvey P. Dale, Aug 09 2021 *)

Extensions

Comment, Mathematica, Crossrefs by Clark Kimberling, Aug 22 2014