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A022426 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 2, a(1) = 3; see Comments. 3
2, 3, 5, 10, 13, 15, 17, 20, 23, 26, 30, 34, 37, 40, 43, 46, 49, 52, 55, 57, 60, 63, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 114, 117, 120, 123, 126, 130, 133, 136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Following the Bode-Harborth-Kimberling link:

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

Ivan Neretin, Table of n, a(n) for n = 0..10000

J-P. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254-264.

MATHEMATICA

Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2, #2 + 1}]]] &, {2, 3}, Range[44]] (* Ivan Neretin, Mar 28 2017 *)

CROSSREFS

Cf. A022424, A299411 (complement).

Sequence in context: A123090 A129281 A289536 * A005677 A162404 A084760

Adjacent sequences:  A022423 A022424 A022425 * A022427 A022428 A022429

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 20 10:17 EDT 2020. Contains 337264 sequences. (Running on oeis4.)