A330116 Beatty sequence for sinh(x), where 1/e^x + csch(x) = 1.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 31, 33, 34, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 76, 78, 79, 81, 82, 84, 85, 87, 88, 89, 91, 92, 94, 95

Offset

1,2

Comments

Let x be the positive solution of 1/e^x + csch(x) = 1. Then (floor(n e^x) and (floor(n sinh(x))) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.

Links

Table of n, a(n) for n=1..66.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n sinh(x)), where x = 1.1676157... is the constant in A330115.

Mathematica

r = x /. FindRoot[1/E^x + Csch[x] == 1, {x, 1, 2}, WorkingPrecision -> 200]
RealDigits[r][[1]] (* A330114 *)
Table[Floor[n*E^r], {n, 1, 250}]  (* A330115 *)
Table[Floor[n*Sinh[r]], {n, 1, 250}]  (* A330116 *)

Crossrefs

Cf. A329825, A330114, A330115 (complement).

Sequence in context: A037087 A320829 A194145 * A189784 A062005 A039018

Adjacent sequences: A330113 A330114 A330115 * A330117 A330118 A330119

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved