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A045681 Extension of Beatty sequence; complement of A045682. 3
0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

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..60.

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

Index entries for sequences related to Beatty sequences

FORMULA

a(n)=mex {a(i), b(i):0<=i<n}, where b=A045682, mex S=least integer >= 0 not in the sequence S.

MATHEMATICA

s=2; t=3;

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}] (* A045681 *)

Table[b[n], {n, 200}] (* A045682 *)

(* From Clark Kimberling, Apr 02 2011 *)

CROSSREFS

Cf. A045671, A045672.

Sequence in context: A172269 A115180 A045774 * A001961 A020656 A039116

Adjacent sequences:  A045678 A045679 A045680 * A045682 A045683 A045684

KEYWORD

nonn

AUTHOR

Aviezri S. Fraenkel

STATUS

approved

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Last modified March 26 05:43 EDT 2019. Contains 321481 sequences. (Running on oeis4.)