suppose i have a set {0,1,2.......x-1}

Now I am generating an i length sequence using the numbers from above set...{a0,a1,....ai} where all ai>=0 and ai<=x-1

Note numbers may repeat in that sequence...so there will be total x^i such sequences.....

Now i am carrying {a0*a1*.......ai}mod x for all such sequences and i get y0,y1 ....and x^i such numbers...

What I want is average value of yi s...can it be generalized for any x and i ?

Guest Jul 7, 2014

#1**+5 **

If I've understood the question correctly (that's a big if!) then there are results listed below for some small values of x. I constructed a numerical algorithm to calculate these values. I haven't been able to think of a generalisation (except when i = 1, in which case y_{1av} = (x-1)/2).

Alan
Jul 7, 2014

#1**+5 **

Best Answer

If I've understood the question correctly (that's a big if!) then there are results listed below for some small values of x. I constructed a numerical algorithm to calculate these values. I haven't been able to think of a generalisation (except when i = 1, in which case y_{1av} = (x-1)/2).

Alan
Jul 7, 2014