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A194145 Beatty sequence for -1+sqrt(6), a(n) = floor(n*(-1+sqrt(6))); complement of A194146. 3

%I #15 Mar 26 2022 17:46:11

%S 1,2,4,5,7,8,10,11,13,14,15,17,18,20,21,23,24,26,27,28,30,31,33,34,36,

%T 37,39,40,42,43,44,46,47,49,50,52,53,55,56,57,59,60,62,63,65,66,68,69,

%U 71,72,73,75,76,78,79,81,82,84,85,86,88,89,91,92,94,95,97,98

%N Beatty sequence for -1+sqrt(6), a(n) = floor(n*(-1+sqrt(6))); complement of A194146.

%C Beatty sequence for 1.449489742783...

%C Beatty sequences occur in complementary pairs; the complement of this is the Beatty sequence for 2+(1/2)*sqrt(6), at A194146.

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

%t r=-1+Sqrt[6];

%t c[k_]:=Floor[k*r];

%t Table[c[k],{k,1,90}] (* A194145 *)

%t s=r/(r-1);

%t d[k_]:=Floor[k*s];

%t Table[d[k],{k,1,90}] (* A194146 *)

%o (Python)

%o from sympy import integer_nthroot

%o def A194145(n): return integer_nthroot(6*n**2,2)[0]-n # _Chai Wah Wu_, Mar 16 2021

%Y Cf. A194146.

%K nonn

%O 1,2

%A _Clark Kimberling_, Aug 17 2011

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Last modified March 2 19:19 EST 2024. Contains 370498 sequences. (Running on oeis4.)