A022840 Beatty sequence for sqrt(6).

2, 4, 7, 9, 12, 14, 17, 19, 22, 24, 26, 29, 31, 34, 36, 39, 41, 44, 46, 48, 51, 53, 56, 58, 61, 63, 66, 68, 71, 73, 75, 78, 80, 83, 85, 88, 90, 93, 95, 97, 100, 102, 105, 107, 110, 112, 115, 117, 120, 122, 124, 127, 129, 132, 134, 137, 139, 142, 144, 146

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Complement of A138235; a(n) = A138236(A138235(n)) and A138236(a(n)) = A138235(n). - Reinhard Zumkeller, Mar 07 2008

Numbers k such that A248515(k+1) = A248515(k) + 1 = 1 + least number h such that 1 - h*sin(1/h) < 1/n^2. The difference sequence of A248515 is (0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, ...), so that A138235 = (1, 3, 5, 6, 8, ...) and A022840 = (2, 4, 7, 9, 12, 14, ...). - Clark Kimberling, Jun 16 2015

Links

• Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
• Clark Kimberling, Beatty sequences and trigonometric functions, Integers 16 (2016), #A15.
• Eric Weisstein's World of Mathematics, Beatty Sequence
• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A010464 (sqrt(6)), A138235 (complement), A248515.

Programs

Haskell

a022840 = floor . (* sqrt 6) . fromIntegral
-- Reinhard Zumkeller, Sep 14 2014

Magma

[Floor(n*Sqrt(6)): n in [1..60]]; // Vincenzo Librandi, Jun 17 2015

Mathematica

Table[Floor[n Sqrt[6]], {n, 70}] (* Vincenzo Librandi, Jun 17 2015 *)

PARI

a(n) = floor(n*sqrt(6)) \\ Iain Fox, Nov 20 2017