

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
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OFFSET

0,2


COMMENTS

(s,t)sequences; the case s=2, t=2.
The sequence can also be characterized by a special numeration systemsee above reference.


LINKS

Table of n, a(n) for n=0..55.
Shiri ArtsteinAvidan, Aviezri S. Fraenkel and Vera T. Sos, A twoparameter family of an extension of Beatty, Discr. Math. 308 (2008), 45784588.
Shiri Artsteinavidan, Aviezri S. Fraenkel and Vera T. Sos, A twoparameter family of an extension of Beatty sequences, Discrete Math., 308 (2008), 45784588.
A. S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics, 2 (1998), 197210.
A. S. Fraenkel, Recent results and questions in combinatorial game complexities, Theoretical Computer Science, vol. 249, no. 2 (2000), 265288.
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, n1}]]];
Table[a[n], {n, 200}] (* A045671 *)
Table[b[n], {n, 200}] (* A045672 *)
(* Clark Kimberling, Apr 02 2011 *)


CROSSREFS

Cf. A026366, A045671.
Sequence in context: A276338 A079774 A276340 * A072473 A072715 A049621
Adjacent sequences: A045669 A045670 A045671 * A045673 A045674 A045675


KEYWORD

nonn


AUTHOR

Aviezri S. Fraenkel


STATUS

approved



