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

1,2

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

Links

Table of n, a(n) for n=1..120.

Formula

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

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 *)

Crossrefs

Cf. A184587.

Sequence in context: A225240 A104309 A306683 * A190511 A260466 A033035

Adjacent sequences: A184583 A184584 A184585 * A184587 A184588 A184589

Keyword

nonn

Author

Clark Kimberling, Jan 17 2011

Extensions

Name and formula corrected by Michel Dekking, Sep 08 2017

Status

approved