A022425 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 1, a(1) = 4; see Comments.

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

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 A363319

Adjacent sequences: A022422 A022423 A022424 * A022426 A022427 A022428

Keyword

nonn

Author

Clark Kimberling

Extensions

Updated by Clark Kimberling, Feb 19 2018

Status

approved