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A299486 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments. 3
1, 2, 3, 15, 18, 21, 24, 27, 30, 33, 36, 39, 43, 47, 52, 56, 61, 65, 70, 74, 79, 83, 88, 92, 97, 101, 106, 110, 115, 119, 123, 127, 131, 135, 139, 143, 147, 150, 154, 158, 162, 166, 170, 174, 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] = 2; a[2] = 3; b[0] = 4; b[1] = 5; 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}]]];

u = Table[a[n], {n, 0, 100}]    (* A299486 *)

v = Table[b[n], {n, 0, 100}]    (* A299487 *)

CROSSREFS

Cf. A022424, A299487.

Sequence in context: A241721 A066491 A282383 * A173334 A331089 A294131

Adjacent sequences:  A299483 A299484 A299485 * A299487 A299488 A299489

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2018

STATUS

approved

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