OFFSET
0,1
COMMENTS
A246393 and A246394 partition A062389 (the nonhomogeneous Beatty sequence {floor(-1/2)*Pi)}. Likewise, A246046, the complement of A062389, is partitioned by A246395 and A246396. (See the Mathematica program.)
Conjecture: every term t has at least one neighbor which is equal to t plus or minus one. - Harvey P. Dale, Jul 11 2023
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
MATHEMATICA
z = 400; f[x_] := Cos[x]
Select[Range[0, z], f[#]*f[# + 1] <= 0 &] (* A062389 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &] (* A246393 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &] (* A246394 *)
Select[Range[0, z], f[#]*f[# + 1] > 0 &] (* A246046 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &] (* A246395 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &] (* A246396 *)
SequencePosition[Table[If[Cos[k]<=0, 1, 0], {k, 200}], {1, 1}][[;; , 1]] (* Harvey P. Dale, Jul 11 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 24 2014
STATUS
approved