A022426 - OEIS

%I #10 Feb 19 2018 22:04:14

%S 2,3,5,10,13,15,17,20,23,26,30,34,37,40,43,46,49,52,55,57,60,63,65,68,

%T 71,74,77,80,83,86,89,92,95,98,101,104,107,110,114,117,120,123,126,

%U 130,133,136

%N Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 2, a(1) = 3; see Comments.

%C Following the Bode-Harborth-Kimberling link:

%C a(n) = b(n-1) + b(n-2) for n > 2;

%C b(0) = least positive integer not in {a(0),a(1)};

%C b(n) = least positive integer not in {a(0),...,a(n),b(0),...,b(n-1)} for n > 1.

%C Note that (b(n)) is strictly increasing and is the complement of (a(n)).

%C See A022424 for a guide to related sequences.

%H Ivan Neretin, <a href="/A022426/b022426.txt">Table of n, a(n) for n = 0..10000</a>

%H J-P. Bode, H. Harborth, C. Kimberling, <a href="https://www.fq.math.ca/Papers1/45-3/bode.pdf">Complementary Fibonacci sequences</a>, Fibonacci Quarterly 45 (2007), 254-264.

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

%Y Cf. A022424, A299411 (complement).

%K nonn

%O 0,1

%A _Clark Kimberling_