A329994 Beatty sequence for 2^x, where 1/x^2 + 1/2^x = 1.

2, 4, 7, 9, 12, 14, 17, 19, 22, 24, 27, 29, 31, 34, 36, 39, 41, 44, 46, 49, 51, 54, 56, 59, 61, 63, 66, 68, 71, 73, 76, 78, 81, 83, 86, 88, 90, 93, 95, 98, 100, 103, 105, 108, 110, 113, 115, 118, 120, 122, 125, 127, 130, 132, 135, 137, 140, 142, 145, 147

Offset

1,1

Comments

Let x be the solution of 1/x^2 + 1/2^x = 1. Then (floor(n x^2)) 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..60.

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 = 1.298192... is the constant in A329992.

Mathematica

r = x /. FindRoot[1/x^2 + 1/2^x == 1, {x, 1, 10}, WorkingPrecision -> 120]
RealDigits[r][[1]] (* A329992 *)
Table[Floor[n*r^2], {n, 1, 250}]  (* A329993 *)
Table[Floor[n*2^r], {n, 1, 250}]  (* A329994 *)

Crossrefs

Cf. A329825, A329992, A329993 (complement).

Sequence in context: A059542 A190324 A022840 * A064995 A329846 A067839

Adjacent sequences: A329991 A329992 A329993 * A329995 A329996 A329997

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Extensions

Formula corrected. - R. J. Mathar, Jan 24 2020

Status

approved