A080081 Beatty sequence for (3+sqrt(13))/2.

3, 6, 9, 13, 16, 19, 23, 26, 29, 33, 36, 39, 42, 46, 49, 52, 56, 59, 62, 66, 69, 72, 75, 79, 82, 85, 89, 92, 95, 99, 102, 105, 108, 112, 115, 118, 122, 125, 128, 132, 135, 138, 142, 145, 148, 151, 155, 158, 161, 165, 168, 171, 175, 178, 181, 184, 188, 191, 194, 198, 201, 204, 208, 211, 214, 217, 221, 224, 227, 231, 234, 237, 241, 244, 247, 251, 254, 257, 260

Offset: 1

Author

N. J. A. Sloane, Mar 15 2003

Keywords

• nonn
• easy

Comments

a(1)=3; for n>1, a(n+1)=a(n)+4 if n is already in the sequence, a(n+1)=a(n)+3 otherwise.

a(n)-1 is the index of the n-th 1 in sequence A276397. - M. F. Hasler, Oct 07 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
• B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
• Eric Weisstein's World of Mathematics, Beatty Sequence.
• Index entries for sequences related to Beatty sequences.

Crossrefs

Cf. A098316.

Differs from A059550 at 76th term.

Programs

Magma

[Floor(n*(3+Sqrt(13))/2): n in [1..80]]; // Vincenzo Librandi, Oct 25 2011

Mathematica

Floor[Range[100]*(3 + Sqrt[13])/2] (* Paolo Xausa, Jul 08 2024 *)

PARI

A080081(n)=n*(3+sqrt(13))\2 \\ M. F. Hasler, Oct 07 2016