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

0,2

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

Table of n, a(n) for n=0..80.

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