A059550 -id:A059550 - cp's OEIS frontend

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

N. J. A. Sloane, Mar 15 2003

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

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.

Cf. A098316.

Differs from A059550 at 76th term.

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

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

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

A059549 Beatty sequence for 1 + 1/log(10).

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 20, 21, 22, 24, 25, 27, 28, 30, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 53, 54, 55, 57, 58, 60, 61, 63, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 78, 80, 81, 83, 84, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100

Offset: 1

Mitch Harris, Jan 22 2001

Harry J. Smith, Table of n, a(n) for n = 1..2000
Aviezri S. Fraenkel, Jonathan Levitt and Michael Shimshoni, Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no.4, 335-345.
Eric Weisstein's World of Mathematics, Beatty Sequence.
Index entries for sequences related to Beatty sequences

Beatty complement is A059550.

Cf. A002285.

Floor[Range[100]*(1 + Log10[E])] (* Paolo Xausa, Jul 05 2024 *)

{ default(realprecision, 100); b=1 + 1/log(10); for (n = 1, 2000, write("b059549.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

a(n) = floor(n*(1 + 1/log(10))). - Michel Marcus, Jan 04 2015

cp's OEIS Frontend

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

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