A330067 Beatty sequence for sinh(x), where 1/x + 1/sinh(x) = 1.

2, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, 40, 42, 45, 47, 50, 53, 55, 58, 60, 63, 65, 68, 70, 73, 75, 78, 80, 83, 85, 88, 90, 93, 95, 98, 100, 103, 106, 108, 111, 113, 116, 118, 121, 123, 126, 128, 131, 133, 136, 138, 141, 143, 146, 148, 151

Offset

1,1

Comments

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

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n sinh(x)), where x = 1.656135560... is the constant in A330065.

Mathematica

r = x /. FindRoot[1/x + 1/Sinh[x] == 1, {x, 2, 10}, WorkingPrecision -> 210]
RealDigits[r][[1]] (* A330065 *)
Table[Floor[n*r], {n, 1, 250}]  (* A330066 *)
Table[Floor[n*Sinh[r]], {n, 1, 250}]  (* A330067 *)

Crossrefs

Cf. A329825, A330065, A330066 (complement).

Sequence in context: A075328 A038126 A047215 * A059536 A030193 A292653

Adjacent sequences: A330064 A330065 A330066 * A330068 A330069 A330070

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved