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Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: computing k-th digit of a real number independently of the previous ones
Replies: 10   Last Post: Jul 1, 2012 4:12 PM

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angel.proorocu@gmail.com

Posts: 3
Registered: 6/21/12
computing k-th digit of a real number independently of the previous ones
Posted: Jun 21, 2012 5:29 PM
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Q: Is it possible to prove the existence of a real number with the property that in order to compute its k-th digit, we must compute all the previous ones?

For example, the k-th digit of PI can be directly computed without going sequentially through the first k-1. I was wondering what is the general case for algebraic numbers - can their k-th digit be computed ignoring the previous ones? Are there any proves that such a real number exists, or on the contrary - that there can't be such a number? How about other transcendental numbers?

Any pointers?

Thanks,

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