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

1,1

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A329834 A059542 A190324 * A329994 A064995 A329846

Adjacent sequences: A022837 A022838 A022839 * A022841 A022842 A022843

Keyword

nonn

Author

Clark Kimberling

Status

approved