A246410 -id:A246410 - cp's OEIS frontend

A246413 Positive integers k satisfying csc(k) > csc(k+1).

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 112, 114, 116, 118, 120, 122, 124, 126

Offset: 1

Clark Kimberling, Aug 25 2014

a(n), A246414, and A246415 partition the positive integers.

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

Cf. A246414, A246415, A246410 (complement of a(n)).

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[130]],2,1],?(#[[1]]>#[[2]]&),1,Heads-> False]// Flatten (* _Harvey P. Dale, Jul 27 2020 *)

A246411 Positive integers k satisfying csc(k) > csc(k+1) < csc(k+2).

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 112, 114, 116, 118, 120, 122, 124, 126, 128

Offset: 1

Clark Kimberling, Aug 25 2014

A246410, a(n), and A246412 partition the positive integers.

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

Cf. A246410, A246412.

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*)

a(n) = A158333(n-1) for n<73. - R. J. Mathar, Sep 01 2014

A246412 Positive integers k satisfying csc(k) > csc(k+1) > csc(k+2) < csc(k+3).

Original entry on oeis.org

44, 88, 132, 199, 243, 287, 331, 377, 421, 465, 509, 532, 576, 620, 664, 710, 754, 798, 842, 909, 953, 997, 1041, 1087, 1131, 1175, 1219, 1242, 1286, 1330, 1374, 1420, 1464, 1508, 1552, 1619, 1663, 1707, 1751, 1797, 1841, 1885, 1929, 1952, 1996, 2040, 2084

Offset: 1

Clark Kimberling, Aug 25 2014

A246410, A246411, and a(n) partition the positive integers.

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

Cf. A246410, A246411.

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*)

cp's OEIS Frontend

A246413 Positive integers k satisfying csc(k) > csc(k+1).

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A246411 Positive integers k satisfying csc(k) > csc(k+1) < csc(k+2).

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A246412 Positive integers k satisfying csc(k) > csc(k+1) > csc(k+2) < csc(k+3).

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