

A022425


Solution a( ) of the complementary equation a(n) = b(n1) + b(n2), 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
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OFFSET

0,2


COMMENTS

a(n) = b(n1) + b(n2) 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(n1)} 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
JP. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254264.


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



