

A045749


Extension of Beatty sequence; complement of A045750.


5



0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68
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OFFSET

0,3


COMMENTS

(s,t)sequences; the case s=3, t=1.
Complement of A045750. It appears likely that A045749(n)=A187570(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), 197210.
Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), #07.1.4.
Index entries for sequences related to Beatty sequences


FORMULA

a(n) = mex {a(i), b(i):0 <= i<n}, where b=A045750, mex S=least integer >= 0 not in the sequence S.


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, n1}]]];
Table[a[n], {n, 200}] (* A045749 *)
Table[b[n], {n, 200}] (* A045750 *)
(* Clark Kimberling, Apr 02 2011 *)


CROSSREFS

Cf. A045681, A045682, A045749, A187570.
Sequence in context: A188292 A171948 A287527 * A187570 A045671 A276341
Adjacent sequences: A045746 A045747 A045748 * A045750 A045751 A045752


KEYWORD

nonn


AUTHOR

Aviezri S. Fraenkel


STATUS

approved



