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A022425 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 1, a(1) = 4; see Comments. 3
1, 4, 5, 9, 13, 15, 18, 21, 23, 26, 30, 33, 36, 39, 42, 46, 49, 52, 55, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 89, 92, 95, 98, 101, 104, 107, 110, 114, 117, 120, 123, 126, 129, 132, 135 (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

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}]]] &, {1, 4}, Range[44]] (* Ivan Neretin, Mar 28 2017 *)

CROSSREFS

Cf. A022424, A299407 (complement).

Sequence in context: A322135 A034705 A006844 * A277549 A331531 A328223

Adjacent sequences:  A022422 A022423 A022424 * A022426 A022427 A022428

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Updated by Clark Kimberling, Feb 19 2018

STATUS

approved

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Last modified August 10 00:24 EDT 2020. Contains 336359 sequences. (Running on oeis4.)