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A329831
Beatty sequence for (7+sqrt(65))/8.
4
1, 3, 5, 7, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 33, 35, 37, 39, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 90, 92, 94, 96, 97, 99, 101, 103, 105, 107, 109, 111, 112, 114, 116, 118
OFFSET
1,2
COMMENTS
Let r = (7+sqrt(65))/8. Then (floor(n*r)) and (floor(n*r + r/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.
FORMULA
a(n) = floor(n*r), where r = (7+sqrt(65))/8.
MATHEMATICA
t = 1/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}] (* A329831 *)
Table[Floor[s*n], {n, 1, 200}] (* A329832 *)
CROSSREFS
Cf. A329825, A329832 (complement).
Sequence in context: A134322 A186328 A063460 * A329938 A247429 A187232
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 31 2019
STATUS
approved