What characteristic do these three 12-digit numbers share with each other, but with no other 12-digit number?
100307124369
111824028801
433800063225
I quickly discovered that all three are perfect squares, being the squares of:
316713, 334401, 658635 respectively.
I was making no further progress with this until I "cheated" by looking in oeis.
This sequence is in oeis, A153749
Numbers k such that there are 12 digits in k^2 and for each factor f of 12 (1,2,3,4,6) the sum of digit groupings of size f is a square.
I would never have noticed this relationship without oeis.
A similar sequence of 6-digit numbers (A258660) is
103041
120409
160801
which are squares of
321
347
401
and whose digit sums taken 1 or 2 or 3 at a time are squares, the factors of 6 being 1,2,3.
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Posted by Larry
on 2024-12-21 12:55:19 |
Solved with some help