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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

(s,t)-sequences; the case s=3, t=2.

LINKS

Table of n, a(n) for n=0..54.

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.

Index entries for sequences related to Beatty sequences

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

Cf. A045749, A045750.

Sequence in context: A039199 A172269 A115180 * A045681 A001961 A020656

Adjacent sequences:  A045771 A045772 A045773 * A045775 A045776 A045777

KEYWORD

nonn

AUTHOR

Aviezri S. Fraenkel

STATUS

approved

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)