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Upper Beatty array of sqrt(3).
1

%I #5 Mar 30 2012 18:57:12

%S 1,2,2,6,4,3,24,15,7,4,104,64,27,9,5,462,283,116,34,11,6,2060,1261,

%T 513,145,43,14,7,9194,5627,2286,641,186,55,16,8,41040,25117,10201,

%U 2856,824,238,63,18,9,183204,112122,45534,12743

%N Upper Beatty array of sqrt(3).

%C Upper and lower Beatty arrays U and L are defined in general at A181661. Notation: U(n,k) and L(n,k) for n>=1 and k>=0.

%C Column 2 of U is A022838, the Beatty sequence of sqrt(3); column 2 of L is the complement, A003511, the Beatty sequence of (1+sqrt(3))/2.

%C U(n,k)-L(n,k)=U(n,1)-L(n,1)=floor(n*r)-floor(n*s) where r=sqrt(3) and s=(1+r)/2.

%e Northwest corner of U:

%e 1....2....6...24...104...

%e 2....4...15...64...283...

%e 3....7...27..116...513...

%e 4....9...34..145...641...

%Y Cf. A181661, A182787.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Dec 02 2010