A172338 a(n) = floor(n*(sqrt(5)+sqrt(3))).

0, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218

Offset: 0

Author

Vincenzo Librandi, Feb 01 2010

Keywords

• nonn
• less
• easy

Comments

sqrt(5)+sqrt(3) = 3.96811878506867... is the largest root of x^4 - 16*x^2 + 4.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A110117, A172323-A172332, A172334, A172336, A172337.

Programs

Magma

[Floor(n*Sqrt(5)+Sqrt(3)): n in [0..60] ];

Mathematica

With[{c = Sqrt[5] + Sqrt[3]}, Floor[c Range[0,60]]] (* Harvey P. Dale, Apr 10 2012 *)

PARI

a(n)=sqrtint(sqrtint(60*n^4)+8*n^2) \\ Charles R Greathouse IV, Jan 24 2022