A003511 A Beatty sequence: floor( n * (1 + sqrt(3))/2 ).

1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 56, 57, 58, 60, 61, 62, 64, 65, 66, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 86, 87, 88, 90, 91, 92, 94, 95, 96

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Matthew House, Table of n, a(n) for n = 1..10000
• Aviezri S. Fraenkel, Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups, Transactions of the American Mathematical Society 341.2 (1994): 639-664.
• Aviezri S. Fraenkel, Jonathan Levitt, 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

Crossrefs

Cf. A003512 (complement).

Programs

Maple

for n from 1 to 200 do printf(`%d,`,floor(n*(1 + sqrt(3))/2 )) od:

Mathematica

Floor[Range[100]*(1 + Sqrt[3])/2] (* Paolo Xausa, Jul 05 2024 *)

Formula

a(n) = floor(n*(1+sqrt(3))/2). - Michel Marcus, Jan 05 2015

Extensions

More terms from James Sellers, Feb 19 2001