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A045774
Extension of Beatty sequence; complement of A045775.
2
0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65
OFFSET
0,3
COMMENTS
(s,t)-sequences; the case s=3, t=2.
LINKS
A. S. Fraenkel, Heap games, numeration systems and sequences, arXiv:math/9809074 [math.CO], 1998; Annals of Combinatorics, 2 (1998), 197-210.
Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13.
Wen An Liu and Xiao Zhao, Adjoining to (s,t)-Wythoff's game its P-positions as moves, Discrete Applied Mathematics, 179 (2014), 28-43. See Table 5.
FORMULA
a(n)=mex {a(i), b(i):0 <= i<n}, where b=A045775, mex S=least integer >= 0 not in the sequence S.
MATHEMATICA
s=3; 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}] (* A045774 *)
Table[b[n], {n, 200}] (* A045775 *)
(* Clark Kimberling, Apr 02 2011 *)
CROSSREFS
Sequence in context: A039199 A172269 A115180 * A045681 A001961 A020656
KEYWORD
nonn
STATUS
approved