cp's OEIS Frontend

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

%I A022425 #12 Jan 05 2025 19:51:34
%S A022425 1,4,5,9,13,15,18,21,23,26,30,33,36,39,42,46,49,52,55,57,60,63,66,69,
%T A022425 72,75,78,81,84,87,89,92,95,98,101,104,107,110,114,117,120,123,126,
%U A022425 129,132,135
%N A022425 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 1, a(1) = 4; see Comments.
%C A022425 a(n) = b(n-1) + b(n-2) for n > 2;
%C A022425 b(0) = least positive integer not in {a(0),a(1)};
%C A022425 b(n) = least positive integer not in {a(0),...,a(n),b(0),...,b(n-1)} for n > 1.
%C A022425 Note that (b(n)) is strictly increasing and is the complement of (a(n)).
%C A022425 See A022424 for a guide to related sequences.
%H A022425 Ivan Neretin, <a href="/A022425/b022425.txt">Table of n, a(n) for n = 0..10000</a>
%H A022425 J-P. Bode, H. Harborth, C. Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/45-3/bode.pdf">Complementary Fibonacci sequences</a>, Fibonacci Quarterly 45 (2007), 254-264.
%t A022425 Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2, #2 + 1}]]] &, {1, 4}, Range[44]] (* _Ivan Neretin_, Mar 28 2017 *)
%Y A022425 Cf. A022424, A299407 (complement).
%K A022425 nonn
%O A022425 0,2
%A A022425 _Clark Kimberling_
%E A022425 Updated by _Clark Kimberling_, Feb 19 2018