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A299420 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 4, a(1) = 5; see Comments. 3
4, 5, 3, 8, 13, 16, 19, 21, 23, 26, 29, 32, 35, 38, 42, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 81, 84, 87, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 162, 165, 168, 171, 174 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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] = 4; 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}]  (* A299420 *)

Table[b[n], {n, 0, 100}]  (* A299421 *)

CROSSREFS

Cf. A022424, A299421.

Sequence in context: A328238 A170929 A245085 * A019836 A020503 A307484

Adjacent sequences:  A299417 A299418 A299419 * A299421 A299422 A299423

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2018

STATUS

approved

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Last modified November 22 00:32 EST 2019. Contains 329383 sequences. (Running on oeis4.)