cp's OEIS Frontend

A079255 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.

%I A079255 #10 Mar 30 2012 18:39:12
%S A079255 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 A079255 66,69,72,75,78,80,83,86,88,91,94,97,100,102,105,108,110,113,116,119,
%U A079255 122,124,127,130,132,135,138,140,143,146,148,151,154,157,160,162,165,168
%N A079255 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 A079255 No two terms in the sequence are consecutive integers (see example for a(3)).
%H A079255 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 A079255 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 A079255 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 A079255 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 A079255 Cf. A079000, A079259. First differences give A080428.
%Y A079255 Cf. A026363, A080428.
%K A079255 easy,nonn
%O A079255 1,2
%A A079255 _N. J. A. Sloane_ and _Matthew Vandermast_, Feb 04 2003