A187570 -id:A187570 - cp's OEIS frontend

A187571 Complement of A187570.

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, 265, 269, 273, 277, 281, 285, 292, 296, 300, 307, 311, 315, 322, 326, 330

Offset: 1

Clark Kimberling, Mar 11 2011

nonn

Is this the same as A045750?

It seems likely; see the comment at A187570.

Cf. A187224, A187570, A045750.

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(See A187570.)
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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

A187571 Complement of A187570.

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