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 A299490 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 1, a(1) = 3, a(2) = 5; see Comments. 3
 1, 3, 5, 12, 17, 21, 24, 27, 30, 34, 38, 42, 45, 49, 53, 57, 61, 65, 70, 74, 79, 83, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 204, 208, 212, 216, 220, 224 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = b(n-1) + b(n-2) + b(n-3) for n > 2; b(0) = least positive integer not in {a(0),a(1),a(2)}; 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..1000 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] = 1; a[1] = 3; a[2] = 5; b[0] = 2; b[1] = 4; b[2] = 6; a[n_] := a[n] = b[n - 1] + b[n - 2] + b[n - 3]; b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]]; Table[a[n], {n, 0, 100}]    (* A299490 *) Table[b[n], {n, 0, 100}]    (* A299491 *) CROSSREFS Cf. A022424, A299491. Sequence in context: A025083 A203150 A237351 * A126471 A317100 A199932 Adjacent sequences:  A299487 A299488 A299489 * A299491 A299492 A299493 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 16 2018 STATUS approved

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Last modified September 20 11:01 EDT 2020. Contains 337264 sequences. (Running on oeis4.)