Consider decimal number 33.
If converted to base 4 form it would be 201, which if regarded as 7 base number would yield 99 decimal.
Pay attention: 99=3*33.
219 is another number displaying the same feature (when converted to base 4 and interpreted as base 7 creates a multiple of the original decimal number).
Please list some additional samples.
Any string of n digits written in base 7 instead of base 4 will be around (7/4)^(n-1) times bigger.
I wrote a little program dividing the string of digits in base 7 and dividing by base 4 an noting when this ratio was an integer.
Base 10 base 4 / 7 base 10 ratio
33 -> 201 -> 99 ratio = 3
(7/4)^2 = 3.0625
219 -> 3123 -> 1095 ratio =5
(7/4)^3 = 5.359
840 -> 31020 -> 7560 ratio = 9
(7/4)^4 = 9.379
1055 -> 100133 -> 16880 ratio = 16
(7/4)^5 = 16.4
Searching up to 6 digits base 4
interestingly there is one solution for each length (none for length 2 or 1)
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Posted by Jer
on 2015-11-03 14:24:44 |
A few
