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regexautomataternary-representation

Ternary Numbers, regex

I'm looking for some regex/automata help. I'm limited to + or the Kleene Star. Parsing through a string representing a ternary number (like binary, just 3), I need to be able to know if the result is 1-less than a multiple of 4.

So, for example 120 = 0*1+2*3+1*9 = 9+6 = 15 = 16-1 = 4(n)-1.

Even a pointer to the pattern would be really helpful!

Solution

  • You can generate a series of values to do some observation with bc in bash: 

    for n in {1..40}; do v=$((4*n-1)); echo -en $v"\t"; echo "ibase=10;obase=3;$v" | bc ; done 

3   10
7   21
11  102
15  120
19  201
23  212
27  1000
31  1011
...