A329835 - OEIS

A329835

Beatty sequence for (9+sqrt(101))/10.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120

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OFFSET

1,2

COMMENTS

Let r = (9+sqrt(101))/10. Then (floor(n*r)) and (floor(n*r + 3r/4)) 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 = (9+sqrt(101))/10.

MATHEMATICA

t = 1/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];

Table[Floor[r*n], {n, 1, 200}] (* A329835 *)

Table[Floor[s*n], {n, 1, 200}] (* A329836 *)

CROSSREFS

Cf. A329825, A329836 (complement).