Re: Finding unique sums.
From: Ryan Reich (ryanr_at_uchicago.edu)
Date: 11/20/04
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Date: Sat, 20 Nov 2004 17:20:46 -0600
matt wrote:
> pradt@yahoo.com (pradeep) wrote in message
> news:<8198af42.0411191652.20eb5bf1@posting.google.com>...
>
>> Hi,
>>
>> I'm trying to find a series where the sum of a subset of that is unique. Or
>> in other words, I can find the numbers from sum.
>>
>> An example would be f(n)=2^n, you add any number of elements in this set,
>> you'll get a number with all those bits set. But I'm looking for a series
>> that does not grow geometrically..
>>
>> Thanks, Pradeep
>
>
> How about ANY series of positive numbers where each term is greater than the
> sum of all those preceding it? Would that work? (Still grows "fast", but not
> necessarily geometrically.)
Actually, that is geometric. Say the first term is a_0. Then the second term
is a_1 > a_0, the third term is a_2 > a_1 + a_0 > 2a_0, the fourth is a_3 > a_2
+ a_1 + a_0 > 2a_0 + a_0 + a_0 = 4a_0, etc. Apply induction if you wish; the
answer is a sequence bounded below by a constant multiple of a geometric sequence.
-- Ryan Reich ryanr@uchicago.edu
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