A026309 - OEIS

%I #12 Dec 11 2024 09:26:57

%S 0,1,5,6,7,11,12,13,17,18,19,24,25,26,30,31,32,36,37,38,42,43,44,45,

%T 49,50,51,55,56,57,61,62,63,68,69,70,74,75,76,80,81,82,86,87,88,89,93,

%U 94,95,99,100,101,105,106,107,112,113,114,118

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

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

%H Clark Kimberling, <a href="/A026309/b026309.txt">Table of n, a(n) for n = 1..4000</a>

%F a(n) ~ 2n by the Equidistribution Theorem. - _Charles R Greathouse IV_, Dec 11 2024

%t z = 500; f[x_] := f[x] = Sin[x]; t = Range[0, z];

%t Select[t, f[#] < f[# + 1] &]  (* A026309 *)

%t Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A246297 *)

%t Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]  (* A246298 *)

%t Select[t, f[#] > f[# + 1] > f[# + 2] > f[# + 3] < f[# + 4] &] (* A246299 *)

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

%K nonn,easy

%O 1,3

%A _Clark Kimberling_

%E Comment, Mathematica, and Crossrefs by _Clark Kimberling_, Aug 21 2014