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Inverse Add
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Posted by: Chris Maes
Reversal Add
Consider the sequence given by
x[n+1] = x[n]+R[x[n],b]
where R[y,b] is the reversal of the digit representation of y in base b, for different initial conditions (integers) x[0].
For instance in base 10, and x[0] = 10 the first five terms in the sequence are
x[0]=10
x[1]=10+01=11
x[2]=11+11=22
x[3]=22+22=44
x[4]=44+44=88
x[5]=88+88=176
In Mathematica this is equivalent to
ReverseAdd[x0_, b_, n_] :=
NestList[(FromDigits[Reverse[IntegerDigits[#, b]], b] + #) &, x0, n]
ReverseAdd[10,10,5]
Wolfram observed that for x[0]=512, no repetitive nature occurred in the base 2 representation of the sequence {x[n]} for the first million iterations.
An earlier initial conditon 271 is equivalent to 512 after 5 iterations. It has been observed that there exits a collection of "attractor" sequences for which many initial conditions converge.
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