A330113 Beatty sequence for cosh(x), where 1/e^x + sech(x) = 1.

1, 3, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 57, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 75, 76, 78, 79, 81, 82, 84, 86, 87, 89, 90, 92, 93, 95, 97, 98, 100, 101

Offset

1,2

Comments

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

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n cosh(x)), where x = 1.01859181977... is the constant in A330111.

Mathematica

r = x /. FindRoot[1/E^x + Sech[x] == 1, {x, 0, 2}, WorkingPrecision -> 200]
RealDigits[r][[1]] (* A330111 *)
Table[Floor[n*E^r], {n, 1, 250}]  (* A330112 *)
Table[Floor[n*Cosh[r]], {n, 1, 250}]  (* A330113 *)
Plot[1/E^x + Sech[x] - 1, {x, -3, 4}]

Crossrefs

Cf. A329825, A330111, A330112 (complement).

Sequence in context: A249117 A093610 A206912 * A329923 A187342 A330143

Adjacent sequences: A330110 A330111 A330112 * A330114 A330115 A330116

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved