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A299407 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 1, a(1) = 4; see Comments. 4
2, 3, 6, 7, 8, 10, 11, 12, 14, 16, 17, 19, 20, 22, 24, 25, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 90, 91, 93, 94, 96, 97, 99, 100 (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] = 1; a[1] = 4; b[0] = 2; b[1] = 3;

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}]  (* A022425 *)

Table[b[n], {n, 0, 100}]  (* A299407 *)

CROSSREFS

Cf. A022424, A022425.

Sequence in context: A028733 A028789 A038100 * A028757 A184798 A047560

Adjacent sequences:  A299404 A299405 A299406 * A299408 A299409 A299410

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 14 2018

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)