A026309 a(n) = n-th nonnegative integer k satisfying sin(k) < sin(k+1).

0, 1, 5, 6, 7, 11, 12, 13, 17, 18, 19, 24, 25, 26, 30, 31, 32, 36, 37, 38, 42, 43, 44, 45, 49, 50, 51, 55, 56, 57, 61, 62, 63, 68, 69, 70, 74, 75, 76, 80, 81, 82, 86, 87, 88, 89, 93, 94, 95, 99, 100, 101, 105, 106, 107, 112, 113, 114, 118

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

The sequences A026309, A246297, A246298, A246299 partition the nonnegative integers.

Links

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

Crossrefs

Cf. A246297, A246298, A246299, A246293 (complement of A026309).

Programs

Mathematica

z = 500; f[x_] := f[x] = Sin[x]; t = Range[0, z];
Select[t, f[#] < f[# + 1] &]  (* A026309 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A246297 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]  (* A246298 *)
Select[t, f[#] > f[# + 1] > f[# + 2] > f[# + 3] < f[# + 4] &] (* A246299 *)

Formula

a(n) ~ 2n by the Equidistribution Theorem. - Charles R Greathouse IV, Dec 11 2024

Extensions

Comment, Mathematica, and Crossrefs by Clark Kimberling, Aug 21 2014