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a(n) = floor(r*n), where r = 4 + sqrt(8); complement of A187394.
4

%I #26 Sep 08 2022 08:45:56

%S 6,13,20,27,34,40,47,54,61,68,75,81,88,95,102,109,116,122,129,136,143,

%T 150,157,163,170,177,184,191,198,204,211,218,225,232,238,245,252,259,

%U 266,273,279,286,293,300,307,314,320,327,334,341,348,355,361,368,375,382,389,396,402,409,416,423,430,437,443,450,457,464,471,477

%N a(n) = floor(r*n), where r = 4 + sqrt(8); complement of A187394.

%C A187393 and A187394 are the Beatty sequences for 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(r*n), where r = 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 [1..100]]; // _Vincenzo Librandi_, Oct 23 2014

%o (Python)

%o from sympy import integer_nthroot

%o def A187393(n): return 4*n+integer_nthroot(8*n**2,2)[0] # _Chai Wah Wu_, Mar 16 2021

%Y Cf. A187394.

%Y A bisection of A001952.

%K nonn

%O 1,1

%A _Clark Kimberling_, Mar 09 2011