A330115 Beatty sequence for e^x, where 1/e^x + csch(x) = 1.

3, 6, 9, 12, 16, 19, 22, 25, 28, 32, 35, 38, 41, 45, 48, 51, 54, 57, 61, 64, 67, 70, 73, 77, 80, 83, 86, 90, 93, 96, 99, 102, 106, 109, 112, 115, 118, 122, 125, 128, 131, 135, 138, 141, 144, 147, 151, 154, 157, 160, 163, 167, 170, 173, 176, 180, 183, 186

Offset

1,1

Comments

Let x be the positive solution of 1/e^x + csch(x) = 1. Then (floor(n e^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..58.

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 = 1.1676157... is the constant in A330115.

Mathematica

r = x /. FindRoot[1/E^x + Csch[x] == 1, {x, 1, 2}, WorkingPrecision -> 200]
RealDigits[r][[1]] (* A330114 *)
Table[Floor[n*E^r], {n, 1, 250}]  (* A330115 *)
Table[Floor[n*Sinh[r]], {n, 1, 250}]  (* A330116 *)

Crossrefs

Cf. A329825, A330114, A330116 (complement).

Sequence in context: A310151 A310152 A189783 * A189513 A194146 A276854

Adjacent sequences: A330112 A330113 A330114 * A330116 A330117 A330118

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved