A267182 Row 2 of the square array in A267181.

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

Offset: 0

Author

N. J. A. Sloane, Jan 17 2016

Keywords

• nonn

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)

Crossrefs

Cf. A267181.

Essentially the same as A097065 and A084964.

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]