A003511 - OEIS

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A003511

A Beatty sequence: floor( n * (1 + sqrt(3))/2 ).
(Formerly M0946)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

FORMULA

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

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 *)

CROSSREFS

Cf. A003512 (complement).

Sequence in context: A079709 A285496 A247778 * A059567 A006594 A172276

Adjacent sequences: A003508 A003509 A003510 * A003512 A003513 A003514