A329829 Beatty sequence for (2+sqrt(10))/3.

1, 3, 5, 6, 8, 10, 12, 13, 15, 17, 18, 20, 22, 24, 25, 27, 29, 30, 32, 34, 36, 37, 39, 41, 43, 44, 46, 48, 49, 51, 53, 55, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 86, 87, 89, 91, 92, 94, 96, 98, 99, 101, 103, 104, 106, 108, 110

Offset

1,2

Comments

Let r = (2+sqrt(10))/3. Then (floor(n*r)) and (floor(n*r + 2r/3)) 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..64.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*r), where r = (2+sqrt(10))/3.

Mathematica

t = 2/3; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329829 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329830 *)

Crossrefs

Cf. A329825, A329830 (complement).

Sequence in context: A083042 A082977 A000210 * A182760 A379805 A292646

Adjacent sequences: A329826 A329827 A329828 * A329830 A329831 A329832

Keyword

nonn,easy

Author

Clark Kimberling, Dec 31 2019

Status

approved