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A299496 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 3, a(1) = 4, a(2) = 5; see Comments. 3
3, 4, 5, 6, 12, 18, 24, 27, 30, 34, 38, 42, 45, 48, 52, 56, 60, 63, 66, 70, 74, 79, 83, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 133, 137, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 187, 191, 196, 200, 204, 208, 212, 216, 220, 224, 228 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From the Bode-Harborth-Kimberling link:

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

Table of n, a(n) for n=0..57.

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; a[2] = 5; b[0] = 1; b[1] = 2; 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}]    (* A299496 *)

Table[b[n], {n, 0, 100}]    (* A299497 *)

CROSSREFS

Cf. A022424, A299497.

Sequence in context: A145735 A228943 A213206 * A070981 A107228 A294247

Adjacent sequences:  A299493 A299494 A299495 * A299497 A299498 A299499

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 21 2018

STATUS

approved

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Last modified May 23 07:08 EDT 2019. Contains 323508 sequences. (Running on oeis4.)