A022840 - OEIS

%I #38 Feb 16 2025 08:32:34

%S 2,4,7,9,12,14,17,19,22,24,26,29,31,34,36,39,41,44,46,48,51,53,56,58,

%T 61,63,66,68,71,73,75,78,80,83,85,88,90,93,95,97,100,102,105,107,110,

%U 112,115,117,120,122,124,127,129,132,134,137,139,142,144,146

%N Beatty sequence for sqrt(6).

%C Complement of A138235; a(n) = A138236(A138235(n)) and A138236(a(n)) = A138235(n). - _Reinhard Zumkeller_, Mar 07 2008

%C 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

%H Iain Fox, <a href="/A022840/b022840.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Reinhard Zumkeller)

%H Clark Kimberling, <a href="https://www.emis.de/journals/INTEGERS/papers/q15/q15.Abstract.html">Beatty sequences and trigonometric functions</a>, Integers 16 (2016), #A15.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%t Table[Floor[n Sqrt[6]], {n, 70}] (* _Vincenzo Librandi_, Jun 17 2015 *)

%o (Haskell)

%o a022840 = floor . (* sqrt 6) . fromIntegral

%o -- _Reinhard Zumkeller_, Sep 14 2014

%o (Magma) [Floor(n*Sqrt(6)): n in [1..60]]; // _Vincenzo Librandi_, Jun 17 2015

%o (PARI) a(n) = floor(n*sqrt(6)) \\ _Iain Fox_, Nov 20 2017

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

%K nonn,changed

%O 1,1

%A _Clark Kimberling_