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%I #10 Mar 30 2012 18:39:12
%S 1,4,6,9,12,15,18,20,23,26,28,31,34,36,39,42,44,47,50,53,56,58,61,64,
%T 66,69,72,75,78,80,83,86,88,91,94,97,100,102,105,108,110,113,116,119,
%U 122,124,127,130,132,135,138,140,143,146,148,151,154,157,160,162,165,168
%N a(n) is taken to be the smallest positive integer greater than a(n-1) such that the condition "n is in the sequence if and only if a(n) is odd and a(n+1) is even" can be satisfied.
%C No two terms in the sequence are consecutive integers (see example for a(3)).
%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a> (math.NT/0305308)
%F With the convention A026363(0)=0 (offset is 1 for this sequence) we have a(n)=A026363(2n)+1; a(n)=(1+sqrt(3))*n+O(1). The sequence satisfies the meta-system for n>=2: a(a(n))=2*a(n)+2*n+2 ; a(a(n)-1)=2*a(n)+2*n-1 ; a(a(n)-2)=2*a(n)+2*n-4 which allows us to have all terms since first differences =2 or 3 only. a(n)=a(n-1)+3 if n is in A026363, a(n)=a(n-1)+2 otherwise (if n is in A026364). - _Benoit Cloitre_, Apr 23 2008
%e a(2) cannot be odd; it also cannot be 2, since that would imply that a(2) was odd. 4 is the smallest value for a(2) that creates no contradiction. a(3) cannot be 5, which would imply that a(5) was odd because it is known from 4's being in the sequence that a(4) is odd and a(5) even. 6 is the smallest value for a(3) that creates no contradiction.
%Y Cf. A079000, A079259. First differences give A080428.
%Y Cf. A026363, A080428.
%K easy,nonn
%O 1,2
%A _N. J. A. Sloane_ and _Matthew Vandermast_, Feb 04 2003
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