login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181661 Upper Beatty array of the golden ratio, (1+sqrt(5))/2. 5
1, 2, 2, 6, 5, 3, 23, 17, 7, 4, 95, 68, 24, 10, 5, 400, 284, 95, 35, 13, 6, 1692, 1199, 396, 141, 46, 15, 7, 7165, 5075, 1671, 590, 186, 53, 18, 8, 30349, 21494, 7072, 2492, 778, 214, 64, 20, 9, 128558, 91046, 29951, 10549, 3286, 896, 259, 71, 23, 10, 544578 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

(row 1)=-1+A049652.

(column 1)=A000027.

(column 2)=A001950=(u(n)), or simply u.

(column 3)=u(u(n))+l(l(n)), or simply uu+ll.

(column 4)=u(uu+ll)+l(ul+lu),

whereas Column 4 of the lower Beatty array

is u(ul+lu)+l(uu+ll).

U(n,k)-L(n,k)=n for n>=1, k>=0.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

Here we introduce Beatty arrays.  Suppose that

((u(1),u(2),...) and (l(1),l(2),...) are the Beatty

sequences of positive real numbers r and s=r/(1-r), where

r<s.  For n>=1, let

U(n,0)=n, U(n,1)=u(1), L(n,0)=0, L(n,1)=l(1),

and for k>=2 let x=floor(r*u(k-1)), y=floor(r*l(k-1)),

a=x+u(k-1), b=x, c=y+l(k-1), d=y,

U(n,k)=a+d, L(n,k)=b+c.  We call U and L the upper and

lower Beatty arrays of r (and of s).  Note that

U(n,k)-L(n,k)=U(n,1)-L(n,1) for all n>=1 and k>=1.

EXAMPLE

Northwest corner of the array:

1.....2.....6....23....95....400...

2.....5....17....68...284...1199...

3.....7....24....95...396...1671...

4....10....35...141...590...2492...

CROSSREFS

Cf. A181886, A000201, A001950, A000045.

Sequence in context: A209773 A209767 A122070 * A144160 A275142 A200226

Adjacent sequences:  A181658 A181659 A181660 * A181662 A181663 A181664

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Nov 18 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 18 16:08 EDT 2017. Contains 290727 sequences.