cp's OEIS Frontend

A187393 a(n) = floor(r*n), where r = 4 + sqrt(8); complement of A187394.

%I A187393 #26 Sep 08 2022 08:45:56
%S A187393 6,13,20,27,34,40,47,54,61,68,75,81,88,95,102,109,116,122,129,136,143,
%T A187393 150,157,163,170,177,184,191,198,204,211,218,225,232,238,245,252,259,
%U A187393 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 A187393 a(n) = floor(r*n), where r = 4 + sqrt(8); complement of A187394.
%C A187393 A187393 and A187394 are the Beatty sequences for r = 4 + sqrt(8) and s = 4 - sqrt(8); 1/r + 1/s = 1.
%C A187393 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 A187393 N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)
%F A187393 a(n) = floor(r*n), where r = 4 + sqrt(8).
%t A187393 r=4+8^(1/2); s=4-8^(1/2);
%t A187393 Table[Floor[r*n],{n,1,80}]  (* A187393 *)
%t A187393 Table[Floor[s*n],{n,1,80}]  (* A187394 *)
%o A187393 (Magma) [Floor (n*(4+Sqrt(8))): n in [1..100]]; // _Vincenzo Librandi_, Oct 23 2014
%o A187393 (Python)
%o A187393 from sympy import integer_nthroot
%o A187393 def A187393(n): return 4*n+integer_nthroot(8*n**2,2)[0] # _Chai Wah Wu_, Mar 16 2021
%Y A187393 Cf. A187394.
%Y A187393 A bisection of A001952.
%K A187393 nonn
%O A187393 1,1
%A A187393 _Clark Kimberling_, Mar 09 2011