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A045672
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Extension of Beatty sequence; complement of A045671.
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5
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| (s,t)-sequences; the case s=2, t=2.
The sequence can also be characterized by a special numeration system-see above reference.
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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.
Shiri Artstein-avidan, Aviezri S. Fraenkel and Vera T. Sos, A two-parameter family of an extension of Beatty sequences, http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/coatp8.pdf, Discrete Math., 308 (2008), 4578-4588.
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LINKS
| A. S. Fraenkel, Heap games, numeration systems and sequences
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
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FORMULA
| b(n)=2a(n)+2n, where a=A045671
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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 2 2011 *)
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CROSSREFS
| Cf. A026366, A045671.
Sequence in context: A098573 A092753 A079774 * A072473 A072715 A049621
Adjacent sequences: A045669 A045670 A045671 * A045673 A045674 A045675
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KEYWORD
| nonn
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AUTHOR
| Aviezri S. Fraenkel (fraenkel(AT)wisdom.weizmann.ac.il)
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