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 A327139 a(n) = n-th 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 17 16:45 EST 2021. Contains 340247 sequences. (Running on oeis4.)