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 A267182 Row 2 of the square array in A267181. 1
 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, 16, 14, 17, 15, 18, 16, 19, 17, 20, 18, 21, 19, 22, 20, 23, 21, 24, 22, 25, 23, 26, 24, 27, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Charlie Neder, Feb 06 2019: (Start) Colin Barker's conjectures below are true. 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) LINKS FORMULA Conjectures from Colin Barker, Jan 29 2016: (Start) a(n) = (1-5*(-1)^n+2*n)/4 for n>0. a(n) = (n-2)/2 for n>0 and even. a(n) = (n+3)/2 for n odd. a(n) = a(n-1)+a(n-2)-a(n-3) for n>3. G.f.: (1+x-3*x^2+2*x^3) / ((1-x)^2*(1+x)). (End) [These are true - see Comments] CROSSREFS Cf. A267181. Sequence in context: A331478 A097065 A084964 * A008720 A340622 A263352 Adjacent sequences:  A267179 A267180 A267181 * A267183 A267184 A267185 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 17 2016 STATUS approved

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Last modified April 20 12:19 EDT 2021. Contains 343135 sequences. (Running on oeis4.)