A330112 Beatty sequence for e^x, where 1/e^x + sech(x) = 1.

2, 5, 8, 11, 13, 16, 19, 22, 24, 27, 30, 33, 36, 38, 41, 44, 47, 49, 52, 55, 58, 60, 63, 66, 69, 72, 74, 77, 80, 83, 85, 88, 91, 94, 96, 99, 102, 105, 108, 110, 113, 116, 119, 121, 124, 127, 130, 132, 135, 138, 141, 144, 146, 149, 152, 155, 157, 160, 163

Offset

1,1

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..59.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n e^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, A330113 (complement).

Sequence in context: A330144 A187341 A329924 * A206911 A093609 A249118

Adjacent sequences: A330109 A330110 A330111 * A330113 A330114 A330115

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved