A329987 Beatty sequence for the number x satisfying 1/x + 1/2^x = 1.

1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 78, 79, 81, 82, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 99, 100

Offset

1,2

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..66.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n x), where x = 1.52980838275... is the constant in A329986.

Mathematica

r = x /. FindRoot[1/x + 1/2^x == 1, {x, 1, 10}, WorkingPrecision -> 210]
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, A329988 (complement).

Sequence in context: A032766 A380408 A189935 * A329962 A258574 A064717

Adjacent sequences: A329984 A329985 A329986 * A329988 A329989 A329990

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved