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A299492 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 2, a(1) = 4, a(2) = 5; see Comments. 3
2, 4, 5, 10, 16, 21, 24, 28, 32, 36, 39, 42, 46, 50, 54, 57, 61, 65, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 115, 119, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 169, 173, 177, 181, 185, 189, 193, 197, 201, 204, 208, 212, 216, 220, 224 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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..56.

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] = 4; a[2] = 5; b[0] = 1; b[1] = 3; 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}]    (* A299492 *)

Table[b[n], {n, 0, 100}]    (* A299493 *)

CROSSREFS

Cf. A022424, A299493.

Sequence in context: A319909 A276281 A059994 * A253198 A138856 A018401

Adjacent sequences:  A299489 A299490 A299491 * A299493 A299494 A299495

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 20 2018

STATUS

approved

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Last modified May 21 00:54 EDT 2019. Contains 323428 sequences. (Running on oeis4.)