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%I #12 Feb 07 2019 12:52:15
%S 1,2,0,3,1,4,2,5,3,6,4,7,5,8,6,9,7,10,8,11,9,12,10,13,11,14,12,15,13,
%T 16,14,17,15,18,16,19,17,20,18,21,19,22,20,23,21,24,22,25,23,26,24,27,
%U 25,28,26,29,27,30,28,31,29,32,30,33,31,34,32,35,33,36,34,37,35,38,36,39,37,40,38,41,39
%N Row 2 of the square array in A267181.
%C From _Charlie Neder_, Feb 06 2019: (Start)
%C _Colin Barker_'s conjectures below are true.
%C Proof: A267181(ka,kb) = A267181(a,b) since both operations preserve the greatest common factor of the two coordinates, so A267181(2k,2) = A267181(k,1) = k for k > 1, the second conjecture. For odd coordinates, we have the forced chain (2k+1,2) -> (2,2k+1) -> (2,2k-1) -> ... -> (2,1) -> (1,2) -> (1,1) with k+3 operations, the third conjecture. The rest follow from combining these. (End)
%F Conjectures from _Colin Barker_, Jan 29 2016: (Start)
%F a(n) = (1-5*(-1)^n+2*n)/4 for n>0.
%F a(n) = (n-2)/2 for n>0 and even.
%F a(n) = (n+3)/2 for n odd.
%F a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.
%F G.f.: (1+x-3*x^2+2*x^3) / ((1-x)^2*(1+x)).
%F (End) [These are true - see Comments]
%Y Cf. A267181.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jan 17 2016
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