

A329845


Beatty sequence for (3+sqrt(29))/5.


3



1, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 20, 21, 23, 25, 26, 28, 30, 31, 33, 35, 36, 38, 40, 41, 43, 45, 46, 48, 50, 51, 53, 55, 57, 58, 60, 62, 63, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 82, 83, 85, 87, 88, 90, 92, 93, 95, 97, 98, 100, 102, 103, 105, 107
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OFFSET

1,2


COMMENTS

Let r = (3+sqrt(29))/5. Then (floor(n*r)) and (floor(n*r + 4r/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



FORMULA

a(n) = floor(n*r), where r = (3+sqrt(29))/5.


MATHEMATICA

t = 4/5; r = Simplify[(2  t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r  1)];
Table[Floor[r*n], {n, 1, 200}] (* A329845 *)
Table[Floor[s*n], {n, 1, 200}] (* A329846 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



