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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 (list; graph; refs; listen; history; text; internal format)
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
Eric Weisstein's World of Mathematics, Beatty Sequence.
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
Cf. A329825, A329846 (complement).
Sequence in context: A188046 A244644 A047220 * A329993 A064994 A138235
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 02 2020
STATUS
approved

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Last modified February 26 12:26 EST 2024. Contains 370352 sequences. (Running on oeis4.)