A258834 Nonhomogeneous Beatty sequence: a(n) = ceiling((n - 1/4)*(2 + sqrt(2))).

0, 3, 6, 10, 13, 17, 20, 24, 27, 30, 34, 37, 41, 44, 47, 51, 54, 58, 61, 65, 68, 71, 75, 78, 82, 85, 88, 92, 95, 99, 102, 105, 109, 112, 116, 119, 123, 126, 129, 133, 136, 140, 143, 146, 150, 153, 157, 160, 164, 167, 170, 174, 177, 181, 184, 187, 191, 194

Offset: 0

Author

Clark Kimberling, Jun 12 2015

Keywords

• nonn
• easy

Comments

Complement of A258833.

See A258833 for more comments.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..10000
• Aviezri S. Fraenkel, The bracket function and complementary sets of integers, Canadian J. of Math. 21 (1969) 6-27.
• Clark Kimberling, Beatty sequences and trigonometric functions, Integers 16 (2016), #A15.

Crossrefs

Cf. A258833 (complement), A184580, A184581.

Programs

Magma

[Ceiling((n-1/4)*(2+Sqrt(2))): n in [0..80]]; // Vincenzo Librandi, Jun 13 2015

Mathematica

r = Sqrt[2]; s = r/(r - 1);
Table[Ceiling[(n + 1/4) r], {n, 0, 100}] (* A258833 *)
Table[Ceiling[(n - 1/4) s], {n, 0, 100}] (* A258834 *)

PARI

vector(60, n, ceil((n-1/4)*(2+sqrt(2)))) \\ G. C. Greubel, Aug 19 2018

Formula

a(n) = ceiling((n - 1/4)*(2 + sqrt(2))) = floor((n - 1/4)*(2 + sqrt(2)) + 1).

Extensions

Corrected by Michel Dekking, Sep 19 2019