|
|
A329838
|
|
Beatty sequence for (6+sqrt(26))/5.
|
|
3
|
|
|
2, 4, 6, 8, 11, 13, 15, 17, 19, 22, 24, 26, 28, 31, 33, 35, 37, 39, 42, 44, 46, 48, 51, 53, 55, 57, 59, 62, 64, 66, 68, 71, 73, 75, 77, 79, 82, 84, 86, 88, 91, 93, 95, 97, 99, 102, 104, 106, 108, 110, 113, 115, 117, 119, 122, 124, 126, 128, 130, 133, 135
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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
|
|
|
FORMULA
|
a(n) = floor(n*s), where s = (6+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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|