A330066 Beatty sequence for x, where 1/x + csch(x) = 1.

1, 3, 4, 6, 8, 9, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 28, 29, 31, 33, 34, 36, 38, 39, 41, 43, 44, 46, 48, 49, 51, 52, 54, 56, 57, 59, 61, 62, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, 81, 82, 84, 86, 87, 89, 91, 92, 94, 96, 97, 99, 101, 102, 104, 105, 107

Offset

1,2

Comments

Let x be the solution of 1/x + csch(x) = 1. Then (floor(n 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..65.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n x), where x = 1.656135560... is the constant in A330065.

Mathematica

r = x /. FindRoot[1/x + 1/Sinh[x] == 1, {x, 2, 10}, WorkingPrecision -> 210]
RealDigits[r][[1]] (* A330065 *)
Table[Floor[n*r], {n, 1, 250}]        (* A330066 *)
Table[Floor[n*Sinh[r]], {n, 1, 250}]  (* A330067 *)

Crossrefs

Cf. A329825, A330065, A330067 (complement).

Sequence in context: A292652 A059535 A061402 * A047206 A187474 A081031

Adjacent sequences: A330063 A330064 A330065 * A330067 A330068 A330069

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved