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

 

Logo

The submissions stack has been unacceptably high for several months now. Please voluntarily restrict your submissions and please help with the editing. (We don't want to have to impose further limits.)

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A045672 Extension of Beatty sequence; complement of A045671. 5
0, 4, 8, 12, 18, 22, 26, 32, 36, 40, 46, 50, 54, 58, 62, 68, 72, 76, 82, 86, 90, 96, 100, 104, 108, 112, 118, 122, 126, 132, 136, 140, 146, 150, 154, 158, 162, 168, 172, 176, 182, 186, 190, 196, 200, 204, 210, 214, 218, 224, 228, 232, 236, 240, 246, 250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(s,t)-sequences; the case s=2, t=2.

The sequence can also be characterized by a special numeration system-see above reference.

LINKS

Table of n, a(n) for n=0..55.

Shiri Artstein-Avidan, Aviezri S. Fraenkel and Vera T. Sos, A two-parameter family of an extension of Beatty, Discr. Math. 308 (2008), 4578-4588.

Shiri Artstein-avidan, Aviezri S. Fraenkel and Vera T. Sos, A two-parameter family of an extension of Beatty sequences, Discrete Math., 308 (2008), 4578-4588.

A. S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics, 2 (1998), 197-210.

A. S. Fraenkel, Recent results and questions in combinatorial game complexities, Theoretical Computer Science, vol. 249, no. 2 (2000), 265-288.

A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.

Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

Index entries for sequences related to Beatty sequences

FORMULA

b(n)=2a(n)+2n, where a=A045671.

MATHEMATICA

s=2; t=2;

mex:=First[Complement[Range[1, Max[#1]+1], #1]]&;

a[0]=0; b[n_]:=b[n]=s*a[n]+t*n;

a[n_]:=a[n]=mex[Flatten[Table[{a[i], b[i]}, {i, 0, n-1}]]];

Table[a[n], {n, 200}] (* A045671 *)

Table[b[n], {n, 200}] (* A045672 *)

(* Clark Kimberling, Apr 02 2011 *)

CROSSREFS

Cf. A026366, A045671.

Sequence in context: A098573 A092753 A079774 * A072473 A072715 A049621

Adjacent sequences:  A045669 A045670 A045671 * A045673 A045674 A045675

KEYWORD

nonn

AUTHOR

Aviezri S. Fraenkel

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified August 29 08:06 EDT 2015. Contains 261188 sequences.