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A003151 Beatty sequence for 1+sqrt(2); a(n) = floor(n*(1+sqrt(2))).
(Formerly M1033)
25

%I M1033

%S 2,4,7,9,12,14,16,19,21,24,26,28,31,33,36,38,41,43,45,48,50,53,55,57,

%T 60,62,65,67,70,72,74,77,79,82,84,86,89,91,94,96,98,101,103,106,108,

%U 111,113,115,118,120,123,125,127,130,132,135,137,140,142,144

%N Beatty sequence for 1+sqrt(2); a(n) = floor(n*(1+sqrt(2))).

%C a(1)=2; for n>1, a(n+1)=a(n)+3 if n is already in the sequence, a(n+1)=a(n)+2 otherwise.

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

%H G. C. Greubel, <a href="/A003151/b003151.txt">Table of n, a(n) for n = 1..5000</a>

%H Shiri Artstein-Avidan, Aviezri S. Fraenkel and Vera T. Sos, <a href="http://dx.doi.org/10.1016/j.disc.2007.08.070">A two-parameter family of an extension of Beatty sequences</a>, Discr. Math. 308 (2008), 4578-4588.

%H Shiri Artstein-avidan, Aviezri S. Fraenkel and Vera T. Sos, <a href="http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/coatp8.pdf">A two-parameter family of an extension of Beatty sequences</a>, Discrete Math., 308 (2008), 4578-4588.

%H L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., <a href="http://www.fq.math.ca/10-5.html">Pellian representatives</a>, Fib. Quart., 10 (1972), 449-488.

%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.

%H J. N. Cooper and A. W. N. Riasanovsky, <a href="http://www.math.sc.edu/~cooper/Sigma.pdf">On the Reciprocal of the Binary Generating Function for the Sum of Divisors</a>, 2012; <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Cooper/cooper3.html">J. Int. Seq. 16 (2013) #13.1.8</a>

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

%p Digits:=100:t:=evalf(1+sec(Pi/4)):A:=n->(t*n):seq(floor((t*n)),n=1..60); # _Zerinvary Lajos_, Mar 27 2009

%t Table[Floor[n*(1 + Sqrt[2])], {n, 1, 50}] (* _G. C. Greubel_, Jul 02 2017 *)

%o (PARI) for(n=1,50, print1(floor(n*(1 + sqrt(2))), ", ")) \\ _G. C. Greubel_, Jul 02 2017

%Y Complement of A003152.

%Y Equals A001951(n) + n.

%Y Cf. A109250.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

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Last modified November 19 11:09 EST 2019. Contains 329319 sequences. (Running on oeis4.)