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A099467 a(1) = a(2) = 1; for n > 2, a(n) is the smallest number > a(n-1) which is not the sum of 2 consecutive elements of the sequence.

%I A099467 #12 Feb 11 2021 03:57:08
%S A099467 1,1,3,5,6,7,9,10,12,14,15,17,18,20,21,23,24,25,27,28,30,31,33,34,36,
%T A099467 37,39,40,42,43,45,46,48,50,51,53,54,56,57,59,60,62,63,65,66,68,69,71,
%U A099467 72,74,75,77,78,80,81,83,84,86,87,89,90,92,93,95,96,97
%N A099467 a(1) = a(2) = 1; for n > 2, a(n) is the smallest number > a(n-1) which is not the sum of 2 consecutive elements of the sequence.
%C A099467 The first differences are 1 and 2 strictly alternately, except near powers of 2: a(2^k+2)-a(2^k+1) = a(2^k+1)-a(2^k). Cf. A001651 which is generated by the same rule if we start from 1, 2 and has first differences 1, 2, 1, 2... with no exceptions. - _Andrey Zabolotskiy_, Feb 11 2021
%H A099467 Robert Israel, <a href="/A099467/b099467.txt">Table of n, a(n) for n = 1..10000</a>
%p A099467 A[1]:= 1: A[2]:= 1: forbid:= {2}:
%p A099467 for n from 3 to 100 do
%p A099467   for k from A[n-1]+1 while member(k, forbid) do od:
%p A099467   A[n]:= k;
%p A099467   forbid:= forbid union {A[n-1]+k};
%p A099467 od:
%p A099467 seq(A[i],i=1..100); # _Robert Israel_, Nov 29 2017
%Y A099467 Cf. A022442 (complement), A001651.
%K A099467 easy,nonn
%O A099467 1,3
%A A099467 Gaetan Polard (gaetan27(AT)hotmail.com), Nov 18 2004