A054406 Beatty sequence for (3+sqrt 3)/2; complement of A022838.

2, 4, 7, 9, 11, 14, 16, 18, 21, 23, 26, 28, 30, 33, 35, 37, 40, 42, 44, 47, 49, 52, 54, 56, 59, 61, 63, 66, 68, 70, 73, 75, 78, 80, 82, 85, 87, 89, 92, 94, 97, 99, 101, 104, 106, 108, 111, 113, 115, 118, 120, 123, 125, 127, 130, 132, 134, 137, 139, 141, 144, 146

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Numbers k such that A194979(k+1) = A194979(k). - Clark Kimberling, Dec 02 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• 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. A194143 (partial sums), A182778 (even bisection), A184799 (prime terms).

Cf. A022838 (complement), A026255.

Cf. A194979.

Programs

Magma

[Floor(n*(3+Sqrt(3))/2): n in [1..70]]; // Vincenzo Librandi, Oct 25 2011

Maple

A054406 := proc(n) n*(3+sqrt(3))/2 ; floor(%) ; end proc: # R. J. Mathar, Feb 26 2011

Mathematica

a054406[n_Integer] := Floor[# (3 + Sqrt[3])/2] & /@ Range[n]; a054406[62] (* Michael De Vlieger, Dec 14 2014 *)

PARI

is(n)=sqrtint((n+1)^2\3)==sqrtint(n^2\3) \\ Charles R Greathouse IV, Nov 01 2021