Find a 7-digit decimal number such that:
It is prime;
Its sod() is 38;
The sod() of the first 3 digits is the reverse of the sod() of the last 3 digits;
When it is converted from decimal to base-N, where N is any integer from 11 to 36, all 10 numeric digits and 23 different letters appear, but there is never a Q, S, or Z in its base-N representation (for those bases).
These constraints determine a unique 7-digit number.
Find it.
Bonus: what is its pop culture significance?
Note: the sod(N) is the sum of digits of N
Set sod(first 3 digits)=10a+b so that 11(a+b)+middle digit=38. Then middle=5 and sod(first 3)=12 or 21.
There are 7 combinations of 3 digits that sum to 21 so I got a list of primes and started checking. I used http://compoasso.free.fr/primelistweb/page/prime/liste_online_en.php
I hoped to find just a handful but my first check found 9935381,9935417,9935543,9935813,9935831 and my second 9395381,9395093,9395147,9395417,9395453,9395471,9395651,9395741.
I gave up at this point as it appeared there would be too many candidates to check base representations by hand without tedium setting in.
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Posted by xdog
on 2023-07-29 08:26:38 |
high hopes dashed
