

A327139


a(n) = nth number k such that cos(2k) > cos(2k+2) < cos(2k+4).


3



1, 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38, 41, 45, 48, 51, 54, 57, 60, 63, 67, 70, 73, 76, 79, 82, 85, 89, 92, 95, 98, 101, 104, 107, 111, 114, 117, 120, 123, 126, 129, 133, 136, 139, 142, 145, 148, 151, 155, 158, 161, 164, 167, 170, 173, 176, 180, 183
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OFFSET

1,2


COMMENTS

The sequences A327138, A327139, A327140 partition the positive integers.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


FORMULA

(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).


MATHEMATICA

z = 500; f[x_] := f[x] = Cos[2 x]; t = Range[1, z];
Select[t, f[#] < f[# + 1] &] (* A327138 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &] (* A327139 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &] (* A327140 *)


CROSSREFS

Cf. A026309, A246303, A026317, A327138.
Sequence in context: A310680 A143457 A046956 * A198265 A310681 A143456
Adjacent sequences: A327136 A327137 A327138 * A327140 A327141 A327142


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Aug 23 2019


STATUS

approved



