A045681 -id:A045681 - cp's OEIS frontend

A045682 Extension of Beatty sequence; complement of A045681.

0, 5, 10, 15, 20, 27, 32, 37, 42, 49, 54, 59, 64, 71, 76, 81, 86, 93, 98, 103, 108, 113, 118, 125, 130, 135, 140, 147, 152, 157, 162, 169, 174, 179, 184, 191, 196, 201, 206, 211, 216, 223, 228, 233, 238, 245, 250, 255, 260, 267, 272, 277, 282, 289, 294, 299

Offset: 0

Aviezri S. Fraenkel

nonn

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

A. S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics, 2 (1998), 197-210.
Index entries for sequences related to Beatty sequences

Cf. A045671, A045672.

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 *)

a(n) = 2*A045681(n)+3*n.

A045749 Extension of Beatty sequence; complement of A045750.

Original entry on oeis.org

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

Offset: 0

Aviezri S. Fraenkel

nonn

(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

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

Cf. A045681, A045682, A045749, A187570.

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 *)

a(n) = mex {a(i), b(i):0 <= iA045750, mex S=least integer >= 0 not in the sequence S.

cp's OEIS Frontend

A045682 Extension of Beatty sequence; complement of A045681.

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