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A003511 A Beatty sequence: floor( n * (1 + sqrt(3))/2 ).
(Formerly M0946)
13

%I M0946 #36 Sep 04 2016 00:54:19

%S 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,

%T 35,36,38,39,40,42,43,45,46,47,49,50,51,53,54,56,57,58,60,61,62,64,65,

%U 66,68,69,71,72,73,75,76,77,79,80,81,83,84,86,87,88,90,91,92,94,95,96

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

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

%H Matthew House, <a href="/A003511/b003511.txt">Table of n, a(n) for n = 1..10000</a>

%H Aviezri S. Fraenkel, <a href="http://dx.doi.org/10.1090/S0002-9947-1994-1138949-9">Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups</a>, Transactions of the American Mathematical Society 341.2 (1994): 639-664.

%H Aviezri S. Fraenkel, Jonathan Levitt, Michael Shimshoni, <a href="http://dx.doi.org/10.1016/0012-365X(72)90012-X">Characterization of the set of values f(n)=[n alpha], n=1,2,...</a>, Discrete Math. 2 (1972), no. 4, 335-345.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>.

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%F a(n) = floor(n*(1+sqrt(3))/2). - _Michel Marcus_, Jan 05 2015

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

%Y Cf. A003512 (complement).

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Feb 19 2001

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)