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A Beatty sequence: a(n) = floor(n*2^sqrt(2)).
4

%I #30 Jan 31 2023 08:39:06

%S 0,2,5,7,10,13,15,18,21,23,26,29,31,34,37,39,42,45,47,50,53,55,58,61,

%T 63,66,69,71,74,77,79,82,85,87,90,93,95,98,101,103,106,109,111,114,

%U 117,119,122,125,127,130,133,135,138,141,143,146,149,151

%N A Beatty sequence: a(n) = floor(n*2^sqrt(2)).

%C 2^sqrt(2) is the Hilbert number (a.k.a. Gelfond-Schneider constant) (A007507).

%C Of course this is different from A047480.

%H G. C. Greubel, <a href="/A038127/b038127.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hilbert_number">Hilbert number</a>

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

%t Floor[2^Sqrt[2] Range[0,60]] (* _Harvey P. Dale_, Dec 03 2012 *)

%o (PARI) for(n=1,50, print1(floor(n*2^(sqrt(2))), ", ")) \\ _G. C. Greubel_, Mar 27 2018

%o (Magma) [Floor(n*2^(Sqrt(2))): n in [1..50]]; // _G. C. Greubel_, Mar 27 2018

%K nonn

%O 0,2

%A _Felice Russo_