When I got to pick a phone number I chose the one ending in 1729,
because it is 'so interesting'.
But as every number maven knows, all numbers are interesting. When we
introduce mathematical induction to the students, I prove that fact:
1 is obviously interesting: smallest counting number, factor of all
integers...
Now suppose that all numbers from 1 to n-1 are interesting, but n is
not interesting. In other words, n is the SMALLEST uninteresting number.
Isn't that interesting!
Henry Rich
Kip Murray wrote:
> I wonder whether 1729 was a number Ramanujan had met before, or merely a
> number
> whose properties he flashed on as soon as he saw it! For a while 1 7 2 9
> will
> be on your personal list of "times I know".
>
> Roger Hui wrote:
>> The problem is that _every_ number has something
>> notable about it, so that each number is "unforgettable"
>> and consequently it's hard to remember any single
>> one of them.
>>
>> 0000 all zeros
>> 0001 first counting number
>> 0002 first prime number
>> 0003 first odd prime
>> 0004 first composite number
>> ...
>> 24 60 #: ?. */ 24 60
>> 1 6
>>
>> 0106 first number greater than 100 with 2 prime factors
>>
>> etc.
>>
>> You have most likely heard of the story about Hardy
>> and Ramanujan. One day Hardy took a taxi to visit
>> Ramanujan. On arriving Hardy told Ramanujan that
>> the taxi had the 4-digit number n on its license plate,
>> a thoroughly unremarkable number. Ramanujan
>> immediately remarked that n is the first number that ... .
>> I forget what n or the property was, something like,
>> n is the first number that can be written as the sum
>> of two perfect cubes in two different ways, something
>> typically Ramanujanish.
>>
>> Yes, that was it:
>>
>> c=: i*i*i=: >:i.200
>> t=: (</~i.200) * +/~c
>> d=: </.~ ,t
>> (2=#&>d)#d
>> +---------+---------------+---------------+---------+--
>> |1729 1729|1092728 1092728|3375001 3375001|4104 4104| ...
>> +---------+---------------+---------------+---------+--
>> <./ {.&> (2=#&>d)#d
>> 1729
>> I. , 1729 = t
>> 11 1609
>> 1 + (#t) #: 11 1609
>> 1 12
>> 9 10
>> +/ 1 12 ^ 3
>> 1729
>> +/ 9 10 ^ 3
>> 1729
>>
>> Now that I have worked out the number I can find the
>> story on the net: http://en.wikipedia.org/wiki/1729_(number)
>>
>> p.s. In my youth, when I needed to remember a (5-digit)
>> number for a time, I would try to compute its largest
>> prime factor by mental calculation. Try it and you'll
>> see why that works.
>>
>>
>>
>> ----- Original Message -----
>> From: Kip Murray <[email protected]>
>> Date: Saturday, August 22, 2009 5:27
>> Subject: Re: [Jprogramming] Unforgettable times
>> To: Programming forum <[email protected]>
>>
>>> To narrow the puzzle,
>>>
>>> times 3 4 5 NB. Unforgettable
>>> 1 6 2 0
>>> 1 8 1 2
>>> 1 2 0 7
>>> timedata i. 1 8 1 2
>>> 4
>>> times i.8
>>> 1 2 3 4
>>> 1 4 1 4
>>> 1 4 2 8
>>> 1 6 2 0
>>> 1 8 1 2
>>> 1 2 0 7
>>> 1 2 3 4
>>> 1 4 1 4
>>>
>>> You are encouraged to choose your own unforgettable times seen
>>> on a 24-hour
>>> digital clock.
>>>
>>>
>>> Kip Murray wrote:
>>>> Who could forget
>>>>
>>>> times 3 4 5
>>>> 1 6 2 0
>>>> 1 8 1 2
>>>> 1 2 0 7
>>>>
>>>> ?
>>>>
>>>> Kip Murray wrote:
>>>>> Write a verb that produces unforgettable times on a 24-hour
>>> digital clock: who
>>>>> could forget an appointment at 12:34 or 14:14 or 14:28
>>> ? It's too bad that
>>>>> 31:41 , 27:18 and 69:31 do not fit on the clock.
>>>>>
>>>>> times 0
>>>>> 1 2 3 4
>>>>> times 0 1
>>>>> 1 2 3 4
>>>>> 1 4 1 4
>>>>> times i. 5
>>>>> 1 2 3 4
>>>>> 1 4 1 4
>>>>> 1 4 2 8
>>>>> 1 2 3 4
>>>>> 1 4 1 4
>>>>> NB. Oh, well, you will do
>>> better than this
>> ----------------------------------------------------------------------
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> ----------------------------------------------------------------------
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