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A045775 Extension of Beatty sequence; complement of A045774. 2
0, 5, 10, 15, 20, 28, 33, 38, 43, 51, 56, 61, 66, 74, 79, 84, 89, 97, 102, 107, 112, 117, 122, 127, 135, 140, 145, 150, 158, 163, 168, 173, 181, 186, 191, 196, 204, 209, 214, 219, 224, 229, 234, 242, 247, 252, 257, 265, 270, 275, 280, 288, 293, 298, 303 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

REFERENCES

Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

LINKS

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

A. S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics, 2 (1998), 197-210.

Wen An Liu and Xiao Zhao, Adjoining to (s,t)-Wythoff's game its P-positions as moves, Discrete Applied Mathematics, 27 August 2014; see Table 5.

Index entries for sequences related to Beatty sequences

FORMULA

a(n) = 3*A045774(n)+2*n.

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 *)

(* From Clark Kimberling, Apr 02 2011 *)

CROSSREFS

Cf. A045749, A045750.

Sequence in context: A313760 A313761 A045682 * A178892 A269805 A206715

Adjacent sequences:  A045772 A045773 A045774 * A045776 A045777 A045778

KEYWORD

nonn

AUTHOR

Aviezri S. Fraenkel

STATUS

approved

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Last modified April 25 11:43 EDT 2019. Contains 322456 sequences. (Running on oeis4.)