The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A045671 Extension of Beatty sequence; complement of A045672. 7
 0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence can also be characterized by a special numeration system-see above reference. (s,t)-sequences; the case s=2, t=2. For n>=1, these are the positions of 1 in the fixed point of the morphism 0->11, 1->1110; see A285671. Conjecture: -1 < n*r - a(n) < 2 for n>=0, where r = (1 + sqrt(17))/4. - Clark Kimberling, May 02 2017 LINKS Shiri Artstein-avidan, Aviezri S. Fraenkel and Vera T. Sós, A two-parameter family of an extension of Beatty sequences, Discrete Math., 308 (2008), 4578-4588. doi:10.1016/j.disc.2007.08.070 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. FORMULA a(n) = mex{a(i), b(i):0 <= i= 0 not in sequence S. a(n) = (1+sqrt(17))/4*n+O(1). - Benoit Cloitre, Apr 23 2008 MATHEMATICA s=2; t=2; mex:=First[Complement[Range[1, Max[#1]+1], #1]]&; a=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 *) s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {1, 1, 1, 0}}] &, {0}, 10]; (* A285671 *) Flatten[Position[s, 0]]; (* A045672 *) Flatten[Position[s, 1]]; (* A045671 *) (* - Clark Kimberling, May 02 2017 *) CROSSREFS Cf. A026366, A045672, A285671. Sequence in context: A287527 A045749 A187570 * A276341 A098572 A001955 Adjacent sequences: A045668 A045669 A045670 * A045672 A045673 A045674 KEYWORD nonn AUTHOR STATUS approved

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

Last modified March 21 08:05 EDT 2023. Contains 361393 sequences. (Running on oeis4.)