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A299419 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 5; see Comments. 3
1, 2, 4, 7, 8, 9, 10, 12, 13, 14, 16, 18, 20, 21, 23, 24, 26, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 53, 55, 56, 58, 59, 61, 62, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = b(n-1) + b(n-2) for n > 2;

b(0) = least positive integer not in {a(0),a(1)};

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..2000

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

a[n_] := a[n] = b[n - 1] + b[n - 2];

b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];

Table[a[n], {n, 0, 100}]  (* A299418 *)

Table[b[n], {n, 0, 100}]  (* A299419 *)

CROSSREFS

Cf. A022424, A299418.

Sequence in context: A285535 A173416 A103254 * A083454 A047542 A121619

Adjacent sequences:  A299416 A299417 A299418 * A299420 A299421 A299422

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2018

STATUS

approved

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Last modified April 9 09:35 EDT 2020. Contains 333344 sequences. (Running on oeis4.)