This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A267182 #14 May 28 2025 13:53:18 %S A267182 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 A267182 16,14,17,15,18,16,19,17,20,18,21,19,22,20,23,21,24,22,25,23,26,24,27, %U A267182 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 A267182 Row 2 of the square array in A267181. %C A267182 From _Charlie Neder_, Feb 06 2019: (Start) %C A267182 _Colin Barker_'s conjectures below are true. %C A267182 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 A267182 Conjectures from _Colin Barker_, Jan 29 2016: (Start) %F A267182 a(n) = (1-5*(-1)^n+2*n)/4 for n>0. %F A267182 a(n) = (n-2)/2 for n>0 and even. %F A267182 a(n) = (n+3)/2 for n odd. %F A267182 a(n) = a(n-1)+a(n-2)-a(n-3) for n>3. %F A267182 G.f.: (1+x-3*x^2+2*x^3) / ((1-x)^2*(1+x)). %F A267182 (End) [These are true - see Comments] %Y A267182 Cf. A267181. %Y A267182 Essentially the same as A097065 and A084964. %K A267182 nonn %O A267182 0,2 %A A267182 _N. J. A. Sloane_, Jan 17 2016