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 A299417 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 4; see Comments. 3
 1, 2, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = b(n-1) + b(n-2) for n > 2; b(0) = least positive integer not in {a(0),a(1)}; b(n) = least positive integer not in {a(0),...,a(n),b(0),...b(n-1)} for n > 1. Note that (b(n)) is strictly increasing and is the complement of (a(n)). See A022424 for a guide to related sequences. LINKS Clark Kimberling, Table of n, a(n) for n = 0..2000 J-P. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254-264. MATHEMATICA mex := First[Complement[Range[1, Max[#1] + 1], #1]] &; a[0] = 3; a[1] = 4; b[0] = 1; b[1] = 2; a[n_] := a[n] = b[n - 1] + b[n - 2]; b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]]; Table[a[n], {n, 0, 100}]  (* A299416 *) Table[b[n], {n, 0, 100}]  (* A299417 *) CROSSREFS Cf. A022424, A299416. Sequence in context: A224778 A286727 A090946 * A047442 A005781 A157850 Adjacent sequences:  A299414 A299415 A299416 * A299418 A299419 A299420 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 15 2018 STATUS approved

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Last modified September 20 10:49 EDT 2020. Contains 337264 sequences. (Running on oeis4.)