A329988 Beatty sequence for 2^x, where 1/x + 1/2^x = 1.

2, 5, 8, 11, 14, 17, 20, 23, 25, 28, 31, 34, 37, 40, 43, 46, 49, 51, 54, 57, 60, 63, 66, 69, 72, 75, 77, 80, 83, 86, 89, 92, 95, 98, 101, 103, 106, 109, 112, 115, 118, 121, 124, 127, 129, 132, 135, 138, 141, 144, 147, 150, 153, 155, 158, 161, 164, 167, 170

Offset

1,1

Comments

Let x be the solution of 1/x + 1/2^x = 1. Then (floor(n x)) and (floor(n 2^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 2^x), where x = 1.52980838275... is the constant in A329986.

Mathematica

r = x /. FindRoot[1/x + 1/2^x == 1, {x, 1, 10}, WorkingPrecision -> 120]
RealDigits[r][[1]] (* A329986 *)
Table[Floor[n*r], {n, 1, 250}]    (* A329987 *)
Table[Floor[n*2^r], {n, 1, 250}]  (* A329988 *)

Crossrefs

Cf. A329825, A329986, A329987 (complement).

Sequence in context: A276877 A329961 A078608 * A189934 A189386 A292661

Adjacent sequences: A329985 A329986 A329987 * A329989 A329990 A329991

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved