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A288119 Lexicographically earliest sequence of distinct nonnegative terms such that, for any i and j >= 0, a(i+j) != a(i) + a(j).

%I A288119 #16 Jun 14 2017 07:14:29
%S A288119 1,0,2,3,5,4,8,7,6,10,9,11,12,14,13,17,16,15,19,18,20,21,23,22,26,25,
%T A288119 24,28,27,29,30,32,31,35,34,33,37,36,38,39,41,40,44,43,42,46,45,47,48,
%U A288119 50,49,53,52,51,55,54,56,57,59,58,62,61,60,64,63,65,66,68
%N A288119 Lexicographically earliest sequence of distinct nonnegative terms such that, for any i and j >= 0, a(i+j) != a(i) + a(j).
%C A288119 If we drop the unicity constraint, then we obtain A059841.
%C A288119 This sequence is a self-inverse permutation of the natural numbers.
%C A288119 a(1+2+2) = a(1) + a(2) + a(2).
%H A288119 Rémy Sigrist, <a href="/A288119/a288119.pdf">First 9 terms, proof of the formula</a>
%H A288119 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A288119 a(n+9) = a(n) + 9 for any n >= 0.
%F A288119 G.f.: (1-x+2*x^2+x^3+2*x^4-x^5+4*x^6-x^7-x^8+3*x^9)/((1-x)*(1-x^9)). - _Robert Israel_, Jun 13 2017
%e A288119 See Links section.
%p A288119 A[0]:= 1: A[1]:= 0: S:= {0,1}:
%p A288119 for n from 2 to 100 do
%p A288119   Forbid:= S union {seq(A[i]+A[n-i],i=1..floor(n/2))};
%p A288119   A[n]:= min( {$1..max(Forbid)+1} minus Forbid);
%p A288119   S:= S union {A[n]};
%p A288119 od:
%p A288119 [seq(A[i],i=0..100)]; # _Robert Israel_, Jun 13 2017
%Y A288119 Cf. A059841.
%K A288119 nonn
%O A288119 0,3
%A A288119 _Rémy Sigrist_, Jun 05 2017