A329837 Beatty sequence for (4+sqrt(26))/5.

1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 40, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 60, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 80, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 101, 103, 105, 107, 109, 111, 112, 114

Offset

1,2

Comments

Let r = (4+sqrt(26))/5. Then (floor(n*r)) and (floor(n*r + 2r/5)) 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..63.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*r), where r = (4+sqrt(26))/5.

Mathematica

t = 2/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}]   (* A329837 *)
Table[Floor[s*n], {n, 1, 200}]   (* A329838 *)

Crossrefs

Cf. A329825, A329838 (complement).

Sequence in context: A262770 A108598 A184808 * A214315 A249098 A287774

Adjacent sequences: A329834 A329835 A329836 * A329838 A329839 A329840

Keyword

nonn,easy

Author

Clark Kimberling, Dec 31 2019

Status

approved