[seqfan] Re: {5, 235, 72335}^2 = {25, 55225, 5232352225}

[franktaw at netscape.net]

You could try looking at the leading digits of the square, instead of 
the trailing digits.
It's a little trickier, because there isn't the simple relationship 
between the number
of digits of the number and the number of digits determined in the 
square, but I
think it might be fruitful.

For example, we can eliminate numbers starting with 3: every square 
from 32
through 38 (an upper bound on a final sequence of primes) starts with 
1.  Likewise,
222^2 = 49824 and 228^2 = 51984, so every square of a number starting 
with 22
starts with 49, 50, or 51; hence 22 is not a possible initial sequence.

For a program it might make sense to use a slightly simpler, less 
powerful approach
to eliminate prefixes.  To test 32 as a prefix, look at 32^2 = 1024, 
33^2 = 1089;
the common initial portion is 10, which is not all primes, so 32 is not 
possible.  This
approach tends to eliminate prefixes one digit later than the previous 
one.

Franklin T. Adams-Watters