A330063 Beatty sequence for x, where 1/x + sech(x) = 1.

1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 27, 29, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 58, 59, 61, 63, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 92, 93, 95, 97, 98, 100, 101, 103, 105

Offset

1,2

Comments

Let x be the solution of 1/x + sech(x) = 1. Then floor(n*x) and floor(n*cosh(x)) define a pair of Beatty sequences indexed by n; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.

First differs from A000201 at a(34) = 54 <> 55. - Peter Munn, Aug 27 2022

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 = 1.61749989... is the constant in A330062.

Mathematica

r = x /. FindRoot[1/x + 1/Cosh[x] == 1, {x, 2, 10}, WorkingPrecision -> 210]
RealDigits[r][[1]] (* A330062 *)
Table[Floor[n*r], {n, 1, 250}]        (* A330063 *)
Table[Floor[n*Cosh[r]], {n, 1, 250}]  (* A330064 *)

Crossrefs

Cf. A000201, A329825, A330062, A330064 (complement).

Sequence in context: A064724 A285676 A085270 * A066096 A000201 A090908

Adjacent sequences: A330060 A330061 A330062 * A330064 A330065 A330066

Keyword

nonn,easy,changed

Author

Clark Kimberling, Jan 04 2020

Status

approved