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A055562 a(n) = least number greater than a(n-1) not the sum of an earlier pair of consecutive terms, a(0) = 2.

%I A055562 #22 Jan 08 2024 09:00:15
%S A055562 2,3,4,6,8,9,11,12,13,15,16,18,19,21,22,24,26,27,29,30,32,33,35,36,38,
%T A055562 39,41,42,44,45,47,48,49,51,52,54,55,57,58,60,61,63,64,66,67,69,70,72,
%U A055562 73,75,76,78,79,81,82,84,85,87,88,90,91,93,94,96,98,99,101,102,104,105
%N A055562 a(n) = least number greater than a(n-1) not the sum of an earlier pair of consecutive terms, a(0) = 2.
%H A055562 Ivan Neretin, <a href="/A055562/b055562.txt">Table of n, a(n) for n = 0..10000</a>
%H A055562 J.-P. Allouche and J. Shallit, <a href="http://www.math.jussieu.fr/~allouche/kreg2.ps">The Ring of k-regular Sequences, II</a>
%H A055562 J.-P. Allouche and J. Shallit, <a href="https://doi.org/10.1016/S0304-3975(03)00090-2">The ring of k-regular sequences, II</a>, Theoret. Computer Sci., 307 (2003), 3-29.
%F A055562 a(n) = A022441(n) - a(n-1) for n > 0.
%F A055562 a(2n) = 3n + 1 + (floor(log_2 n) mod 2), n >= 1; a(2n+1) = 3n+3, n >= 0. - _Jeffrey Shallit_, Jun 08 2000
%F A055562 a(n) = A210770(2*n+2). - _Reinhard Zumkeller_, Mar 25 2012
%e A055562 a(2) = 4 because a(1) = 3 and 4 <> a(0)+a(1);
%e A055562 a(3) = 6 because a(2) = 4 and 5 = a(0)+a(1) but 6 <> a(0)+a(1) and 6 <> a(1)+a(2).
%Y A055562 Complement of A022441. See A001651 for a(0) = 1 and A055563 for a(0) = 3
%K A055562 nonn
%O A055562 0,1
%A A055562 _Henry Bottomley_, May 26 2000