A330064 Beatty sequence for cosh(x), where 1/x + sech(x) = 1.

2, 5, 7, 10, 13, 15, 18, 20, 23, 26, 28, 31, 34, 36, 39, 41, 44, 47, 49, 52, 55, 57, 60, 62, 65, 68, 70, 73, 75, 78, 81, 83, 86, 89, 91, 94, 96, 99, 102, 104, 107, 110, 112, 115, 117, 120, 123, 125, 128, 130, 133, 136, 138, 141, 144, 146, 149, 151, 154, 157

Offset

1,1

Comments

Let x be the solution of 1/x + sech(x) = 1. Then (floor(n x) and (floor(n cosh(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..60.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n x), where x = 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. A329825, A330062, A330063 (complement).

Sequence in context: A292645 A001950 A090909 * A022841 A038127 A047480

Adjacent sequences: A330061 A330062 A330063 * A330065 A330066 A330067

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved