A246415 Positive integers k satisfying csc(k) < csc(k+1) < csc(k+2) > csc(k+3).

22, 66, 110, 154, 177, 221, 265, 309, 355, 399, 443, 487, 554, 598, 642, 686, 732, 776, 820, 864, 887, 931, 975, 1019, 1065, 1109, 1153, 1197, 1264, 1308, 1352, 1396, 1442, 1486, 1530, 1574, 1597, 1641, 1685, 1729, 1775, 1819, 1863, 1907, 1974, 2018, 2062

Offset: 1

Author

Clark Kimberling, Aug 25 2014

Keywords

• nonn
• easy

Comments

A246413, A246414, and this sequence partition the positive integers.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A246413, A246414.

Programs

Mathematica

z = 200;
f[x_] := f[x] = Csc[x];
Select[Range[1, z], f[#] > f[# + 1] &]  (* A246413 *)
Select[Range[1, z], f[#] < f[# + 1] > f[# + 2] &]  (* A246414 *)
Select[Range[1, z], f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (* A246415 *)

PARI

is(n) = (1/sin(n)) < (1/sin(n+1)) && (1/sin(n+1)) < (1/sin(n+2)) && (1/sin(n+2)) > (1/sin(n+3)) \\ Felix Fröhlich, Jan 02 2018

Extensions

Name corrected by David Gross, Jan 02 2018