[seqfan] Re: numbers whose cube is a palindrome
Robert Munafo
mrob27 at gmail.com
Wed May 18 11:12:11 CEST 2011
I arbitrarily define the limits at 10^6 and 10^1000000 (ten to the power of
one million), making anything with 7 to a million digits a class-2 number
[1]. That's just based on the semi-logical idea that the boundaries between
classes should correspond to limits of the human mind, that each should be
10 to the power of the one before it, and George Miller's "magical number
seven plus or minus two".
But really, the limits depend on what you want to do with the number. If you
are computing the cube by explicitly multiplying out the digits, and
checking the result to see if it is a palindrome, then the limit is related
to how many digits the computer can hold in memory and what kind of
multiplication algorithm is being used.
But, if you're stating a conjecture ("I also think that the next term
appears already in class-2
numbers") it's probably better to use an explicit limit like "less than
1000000 digits" to avoid confusion. I think the "number classes" idea has
little use beyond general discussions about the comprehension of large
numbers.
- Robert Munafo
[1] http://mrob.com/pub/math/largenum.html#class2
[2] George Miller, The magical number seven plus or minus two: some limits
on our capacity for processing information. The Psychological Review 63
(1956), pp. 81-97
On Wed, May 18, 2011 at 01:45, Matevž Markovič
<matevz.markovic.v at gmail.com>wrote:
> Where is exactly the limit for class-2 numbers?
> Above 10^10000 ?
>
> Anyway, did you two search only among those numbers, which are constructed
> with digits {0,1,2}?
>
> Thank you !
>
> Matevž Markovič
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