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A299531 Solution a( ) of the complementary equation a(n) = 2*b(n-1) + b(n-2), where a(0) = 1, a(1) = 2; see Comments. 3
1, 2, 11, 14, 17, 20, 23, 26, 29, 34, 38, 43, 47, 52, 56, 61, 65, 70, 74, 79, 83, 88, 92, 95, 98, 103, 107, 110, 115, 119, 122, 125, 130, 134, 137, 142, 146, 149, 152, 157, 161, 164, 169, 173, 176, 179, 184, 188, 191, 196, 200, 203, 206, 211, 215, 218, 223 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From the Bode-Harborth-Kimberling link:

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

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

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] = 1; a[1] = 2; b[0] = 3; b[1] = 4;

a[n_] := a[n] = 2*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}]    (* A299531 *)

Table[b[n], {n, 0, 100}]    (* A299532 *)

CROSSREFS

Cf. A022424, A299532.

Sequence in context: A073914 A266991 A041971 * A106660 A130288 A287395

Adjacent sequences:  A299528 A299529 A299530 * A299532 A299533 A299534

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 21 2018

STATUS

approved

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