Re: [math-fun] Pick any 4 successive terms a, b, c, d and have a/b = c/d.

12 Oct 2019

      For #1, in case it helps, I think the general term is given by (starting at
0)

a^Floor[1 - i/2] b^(Mod[i, 2]) c^Floor[i/2]

or alternatively,

(c/a)^Floor[i/2] * (a if i is even, otherwise b).

For example, starting with 2, 1, 6,

In[10]:= Table[2^Floor[1 - i/2]1^(Mod[i,2]) 6^Floor[i/2],{i,0,10}]
Out[10]= {2,1,6,3,18,9,54,27,162,81,486}

I think this implies that the sequence will consist of integers so long as a
divides c, though I'm not sure how to handle the requirement that all of the
integers in the sequence be unique.

Thanks!

--Neil Bickford