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A299491 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 1, a(1) = 3, a(2) = 5; see Comments. 3
2, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 89 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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] = 3; a[2] = 5; b[0] = 2; b[1] = 4; 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}]    (* A299490 *)

v = Table[b[n], {n, 0, 100}]    (* A299491 *)

CROSSREFS

Cf. A022424, A299490.

Sequence in context: A039240 A039183 A039136 * A039098 A015860 A147613

Adjacent sequences:  A299488 A299489 A299490 * A299492 A299493 A299494

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2018

STATUS

approved

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Last modified November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)