A246298 Numbers k such that sin(k) > sin(k+1) > sin(k+2) < sin(k+3).

3, 9, 15, 22, 28, 34, 40, 47, 53, 59, 66, 72, 78, 84, 91, 97, 103, 110, 116, 122, 128, 135, 141, 147, 154, 160, 166, 172, 179, 185, 191, 197, 204, 210, 216, 223, 229, 235, 241, 248, 254, 260, 267, 273, 279, 285, 292, 298, 304, 311, 317, 323, 329, 336, 342

Offset: 1

Author

Clark Kimberling, Aug 21 2014

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..1000

Crossrefs

Cf. A246297, 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 *)
Flatten[Position[Partition[Sin[Range[350]],4,1],?(#[[1]]>#[[2]]>#[[3]]<#[[4]]&),1,Heads->False]] (* _Harvey P. Dale, Aug 03 2017 *)

PARI

q(n)=my(s0=sin(n),s1=sin(n+1),s2=sin(n+2),s3=sin(n+3));if( (s0>s1) && (s1>s2) && (s2Joerg Arndt, Aug 03 2017

PARI

list(lim)=my(v=List(),u=vector(4,x,sin(x+2))); forstep(k=3,lim-3,4, u[4]=sin(k+3); if(u[1]>u[2]&&u[2]>u[3]&&u[3]u[3]&&u[3]>u[4]&&u[4]u[4]&&u[4]>u[1]&&u[1]u[1]&&u[1]>u[2]&&u[2]sin(k+1)&&sin(k+1)>sin(k+2)&&sin(k+2)Charles R Greathouse IV, Aug 03 2017

Python

from sympy import sin
def ok(n):
    s0, s1, s2, s3 = sin(n), sin(n + 1), sin(n + 2), sin(n + 3)
    return s0>s1 and s1>s2 and s2Indranil Ghosh, Aug 03 2017

Extensions

Name corrected by Harvey P. Dale, Aug 03 2017