A246413 -id:A246413 - cp's OEIS frontend

A246410 Positive integers k satisfying csc(k) < csc(k+1).

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 111, 113, 115, 117, 119, 121, 123

Offset: 1

Clark Kimberling, Aug 25 2014

Every positive integer is in exactly one of the sequences A246410, A246411, and A246412.

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

Cf. A246411, A246412, A246413 (complement of a(n)).

z = 200; f[x_] := f[x] = Csc[x];
Select[Range[1, z], f[#] < f[# + 1] &] (*A246410*)
Select[Range[1, z], f[#] > f[# + 1] < f[# + 2] &] (*A246411*)
Select[Range[1, 10 z], f[#] > f[# + 1] > f[# + 2] < f[# + 3] &] (*A246412*)

A246414 Positive integers k satisfying csc(k) < csc(k+1) > csc(k+2).

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129

Offset: 1

Clark Kimberling, Aug 25 2014

A246413, a(n), and A246415 partition the positive integers.

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

Cf. A246413, A246415.

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*)
Position[Partition[Csc[Range[200]],3,1],?(#[[1]]<#[[2]]>#[[3]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, May 05 2023 *)

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

Original entry on oeis.org

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

Clark Kimberling, Aug 25 2014

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

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

Cf. A246413, A246414.

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 *)

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

Name corrected by David Gross, Jan 02 2018

cp's OEIS Frontend

A246410 Positive integers k satisfying csc(k) < csc(k+1).

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A246414 Positive integers k satisfying csc(k) < csc(k+1) > csc(k+2).

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

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