A Conversation for Mersenne Numbers
Re: Interesting 1s
ZiGGY^ Started conversation Feb 3, 2002
Multiplying by the base (2) then subtracting 1 and getting continuous 1s is as interesting as 10^n -1 giving lots of 9s (assuming n>0 & is an integer). I personally do not find that interesting but that is my opinion.
Re: Interesting 1s
Bez (arguaby the finest figure of a man ever found wearing Bez's underwear) <underpants> Posted Sep 22, 2003
For (x^n)-1 the answer in base x will always be a number of digits equal to n, all of which are x-1.
eg/
(2^8)-1 in base 2 (binary) = 11111111
(8^4)-1 in base 8 (octal) = 7777
(10^7)-1 in base 10 (normal) = 9999999
(16^9)-1 in base 16 (hexidecimal) = fffffffff
The brackets aren't strictly neccesary, but it makes it a little easier to read since we can't superscript in forums.
Bez
Re: Interesting 1s
Gnomon - time to move on Posted Sep 7, 2010
It's interesting because of the proof based on it later.
Re: Interesting 1s
ITIWBS Posted Sep 9, 2010
A higher math point, take any number of the form:
(b to the nth) - 1
where 'b' is the base and both 'b' and 'n' are always whole positive numbers,
that number is always written in that base in 'n' places filled by the digit representing (b - 1)
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Re: Interesting 1s
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