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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.

REFERENCES

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

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

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

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 *)

(* From 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

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Last modified April 16 00:31 EDT 2014. Contains 240534 sequences.