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A299546 Solution b( ) of the complementary equation a(n) = b(n-1) + 2*b(n-2) - b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments. 3
4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 21, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 50, 52, 53, 54, 57, 59, 60, 62, 63, 64, 67, 68, 70, 71, 72, 75, 76, 78, 79, 80, 83, 84, 86, 87, 88, 91, 92, 94, 95, 96, 98, 100, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From the Bode-Harborth-Kimberling link:

a(n) = b(n-1) + 2*b(n-2) - 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] = 1; a[1] = 2; a[2] = 3; b[0] = 4; b[1] = 5;

a[n_] := a[n] = b[n - 1] + 2 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}]    (* A299545 *)

Table[b[n], {n, 0, 100}]    (* A299546 *)

CROSSREFS

Cf. A022424, A299545.

Sequence in context: A039174 A016069 A194283 * A039128 A214421 A294237

Adjacent sequences:  A299543 A299544 A299545 * A299547 A299548 A299549

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 01 2018

STATUS

approved

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Last modified September 20 11:25 EDT 2020. Contains 337264 sequences. (Running on oeis4.)