Cyclic number-16 digits- Finding multipliers

In my blog posted on 28 feb 2012,I had mentioned about the following multipliers which make the digits at the end move to the front in the cyclic number  0588235294117647-
1,12,8,11,13,3,2,7...16,5,9,6,4,14,15,10
The second number 12 can be used in another way to find the subsequent multipliers-
The digits 1 and 2 in this number 12 have to be used as follows-
Using any two consecutive numbers in the list say m(1) and m(2),the next number can be found by working out 1*m(1)+2*m(2)
Thus taking m(1)=1 and m(2) =12 we find the next number as 1*1+2*12=25 which reduces to 8 after deducting 17 the generator of the cyclic number.
Again using m(1)=12 and m(2)=8,we find the next number as 1*12+2*8=28 which reduces to 11 after deducting 17 as before.
The next number 13 comes out in a similar way viz 1*8+2*11=30 which reduces to 13 after deducting 17
Next number 1*11+2.13=37 which reduces to 3 after deducting 17 twice
Next number is 1*13+2*3=19 which reduces to 2 as before.
All numbers are found similarly
For example using 4 and 14 the next number will be 1*4+2*14=32 which reduces to 15.