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 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 (list; graph; refs; listen; history; text; internal format)
 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 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. FORMULA a(n) = mex {a(i), b(i):0 <= i= 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, n-1}]]]; 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 STATUS approved

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Last modified April 20 08:49 EDT 2019. Contains 322306 sequences. (Running on oeis4.)