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A329840 Beatty sequence for (9+sqrt(41))/4. 3
3, 7, 11, 15, 19, 23, 26, 30, 34, 38, 42, 46, 50, 53, 57, 61, 65, 69, 73, 77, 80, 84, 88, 92, 96, 100, 103, 107, 111, 115, 119, 123, 127, 130, 134, 138, 142, 146, 150, 154, 157, 161, 165, 169, 173, 177, 180, 184, 188, 192, 196, 200, 204, 207, 211, 215, 219 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Let r = (-1+sqrt(41))/4. Then (floor(n*r)) and (floor(n*r + 5r/2)) 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*s), where s = (9+sqrt(41))/4. - corrected by Michael De Vlieger, Aug 27 2021
MATHEMATICA
t = 5/2; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
Table[Floor[r*n], {n, 1, 200}] (* A329839 *)
Table[Floor[s*n], {n, 1, 200}] (* A329840 *)
CROSSREFS
Cf. A329825, A329839 (complement).
Sequence in context: A124981 A249244 A059554 * A329977 A246171 A184422
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 31 2019
STATUS
approved

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Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)