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A299538 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-3), where a(0) = 2, a(1) = 3, a(2) = 4; see Comments. 2
1, 5, 6, 8, 9, 10, 11, 12, 14, 16, 17, 19, 21, 23, 24, 26, 27, 29, 30, 32, 33, 34, 36, 37, 39, 40, 41, 43, 44, 46, 47, 48, 50, 52, 53, 54, 56, 58, 59, 60, 62, 64, 65, 67, 68, 70, 72, 73, 74, 76, 78, 79, 81, 82, 84, 86, 87, 88, 90, 92, 93, 95, 96, 98, 99, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From the Bode-Harborth-Kimberling link:

a(n) = b(n-1) + b(n-3) for n > 3;

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..65.

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] = 2; a[1] = 3; a[2] = 4; b[0] = 1; b[1] = 5;

a[n_] := a[n] = b[n - 1] + 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}]    (* A022437 *)

Table[b[n], {n, 0, 100}]    (* A299538 *)

CROSSREFS

Cf. A022424, A299537.

Sequence in context: A180443 A205705 A270653 * A201512 A242290 A296562

Adjacent sequences:  A299535 A299536 A299537 * A299539 A299540 A299541

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 25 2018

STATUS

approved

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Last modified September 20 11:26 EDT 2020. Contains 337264 sequences. (Running on oeis4.)