A182786 Upper Beatty array of sqrt(3).

1, 2, 2, 6, 4, 3, 24, 15, 7, 4, 104, 64, 27, 9, 5, 462, 283, 116, 34, 11, 6, 2060, 1261, 513, 145, 43, 14, 7, 9194, 5627, 2286, 641, 186, 55, 16, 8, 41040, 25117, 10201, 2856, 824, 238, 63, 18, 9, 183204, 112122, 45534, 12743

Offset

1,2

Comments

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.

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.

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.

Links

Table of n, a(n) for n=1..49.

Example

Northwest corner of U:
1....2....6...24...104...
2....4...15...64...283...
3....7...27..116...513...
4....9...34..145...641...

Crossrefs

Cf. A181661, A182787.

Sequence in context: A134458 A193819 A356790 * A343187 A009279 A059943

Adjacent sequences: A182783 A182784 A182785 * A182787 A182788 A182789

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 02 2010

Status

approved