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%I #23 Sep 08 2022 08:45:56
%S 1,2,3,4,5,7,8,9,10,11,12,14,15,16,17,18,19,21,22,23,24,25,26,28,29,
%T 30,31,32,33,35,36,37,38,39,41,42,43,44,45,46,48,49,50,51,52,53,55,56,
%U 57,58,59,60,62,63,64,65,66,67,69,70,71,72,73,74,76,77,78,79,80,82,83,84,85,86,87,89,90,91,92,93,94,96,97,98,99,100,101,103,104,105,106,107,108,110,111,112,113,114,115,117
%N a(n) = floor(s*n), where s = 4 - sqrt(8); complement of A187393.
%C A187393 and A187394 are the Beatty sequences based on r = 4 + sqrt(8) and s = 4 - sqrt(8); 1/r + 1/s = 1.
%C Let u = 1 + sqrt(2) and v = -1 + sqrt(2). Let U = {h*u, h >= 1} and V = {k*v, k >= 1}. Then A187393(n) is the position of n*u in the ordered union of U and V, and A187394 is the position of n*v. - _Clark Kimberling_, Oct 21 2014
%H N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)
%F a(n) = floor(s*n), where s = 4 - sqrt(8).
%t r=4+8^(1/2); s=4-8^(1/2);
%t Table[Floor[r*n],{n,1,80}] (* A187393 *)
%t Table[Floor[s*n],{n,1,80}] (* A187394 *)
%o (Magma) [Floor (n*(4-Sqrt(8))): n in [0..100]]; // _Vincenzo Librandi_, Oct 23 2014
%o (Python)
%o from sympy import integer_nthroot
%o def A187394(n): return 4*n-1-integer_nthroot(8*n**2,2)[0] # _Chai Wah Wu_, Mar 16 2021
%Y Cf. A187393.
%K nonn
%O 1,2
%A _Clark Kimberling_, Mar 09 2011
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