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A045750 Extension of Beatty sequence, complement of A045749. 6
0, 4, 8, 12, 19, 23, 27, 34, 38, 42, 49, 53, 57, 61, 65, 69, 76, 80, 84, 91, 95, 99, 106, 110, 114, 118, 122, 126, 133, 137, 141, 148, 152, 156, 163, 167, 171, 175, 179, 183, 190, 194, 198, 205, 209, 213, 220, 224, 228, 235, 239, 243, 250, 254, 258 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(s,t)-sequences; the case s=3, t=1.

Complement of A187749.  It appears likely that A045750(n)=A187571(n) for all n>=1; the equation has been verified for n up to 500. - Clark Kimberling, Apr 02 2011

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), #07.1.4.

Index entries for sequences related to Beatty sequences

FORMULA

a(n) = 3*A045749(n) + n.

MATHEMATICA

s=3; t=1;

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}] (* A045749 *)

Table[b[n], {n, 200}] (* A045750 *)

(* Clark Kimberling, Apr 02 2011 *)

CROSSREFS

Cf. A045671, A045672, A187571.

Sequence in context: A311645 A311646 A311647 * A187571 A287402 A311648

Adjacent sequences:  A045747 A045748 A045749 * A045751 A045752 A045753

KEYWORD

nonn

AUTHOR

Aviezri S. Fraenkel

STATUS

approved

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Last modified April 24 16:26 EDT 2019. Contains 322430 sequences. (Running on oeis4.)