A184586 a(n) = floor((n-1/2)*r), where r=sqrt(5); complement of A184587.

1, 3, 5, 7, 10, 12, 14, 16, 19, 21, 23, 25, 27, 30, 32, 34, 36, 39, 41, 43, 45, 48, 50, 52, 54, 57, 59, 61, 63, 65, 68, 70, 72, 74, 77, 79, 81, 83, 86, 88, 90, 92, 95, 97, 99, 101, 103, 106, 108, 110, 112, 115, 117, 119, 121, 124, 126, 128, 130, 133, 135, 137, 139, 141, 144, 146, 148, 150, 153, 155, 157, 159, 162, 164, 166, 168, 171, 173, 175, 177, 180, 182, 184, 186, 188, 191, 193, 195, 197, 200, 202, 204, 206, 209, 211, 213, 215, 218, 220, 222, 224, 226, 229, 231, 233, 235, 238, 240, 242, 244, 247, 249, 251, 253, 256, 258, 260, 262, 264, 267

Offset: 1

Author

Clark Kimberling, Jan 17 2011

Keywords

• nonn

Comments

r = sqrt(5) and s = (5+sqrt(5))/4 form a Beatty pair. This yields the pair of complementary homogeneous Beatty sequences A022839 and A108598. From a theorem of Thoralf Skolem follows that (a(n)) and A184587 are complementary inhomogeneous Beatty sequences. - Michel Dekking, Sep 08 2017

Crossrefs

Cf. A184587.

Programs

Mathematica

r=5^(1/2); c=1/2; s=r/(r-1);
Table[Floor[n*r-c*r],{n,1,120}]  (* A184586 *)
Table[Floor[n*s+c*s],{n,1,120}]  (* A184587 *)

Formula

a(n)=floor[(n-1/2)r], where r=sqrt(5).

Extensions

Name and formula corrected by Michel Dekking, Sep 08 2017