Determining a formula for a (sub)sequence

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SUMMARY

The discussion focuses on deriving a formula for a non-finite subsequence from the first 125,256 terms of a sequence of natural numbers. The user identifies that the distribution is neither linear nor likely polynomial, suggesting the potential involvement of a root function. The sequence is defined by the local maxima of the magnitudes of partial sums of complex-valued terms, specifically where | ∑_{k=0}^{n} a_{k}z^{k} | reaches a maximum.

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  • Understanding of complex analysis, particularly series and partial sums.
  • Familiarity with sequences and subsequences in mathematical terms.
  • Knowledge of root functions and their applications in mathematical sequences.
  • Experience with mathematical modeling and formula derivation techniques.
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  • Research methods for identifying local maxima in complex-valued sequences.
  • Explore techniques for deriving formulas from large datasets of natural numbers.
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Mathematicians, data scientists, and researchers involved in sequence analysis, particularly those seeking to derive formulas from large sets of numerical data.

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I currently have the first 125,256 terms of a sequence of natural numbers. I need to find a formula for any non-finite sub-sequence.

Are there any good methods for obtaining such a formula? I can already say that it isn't a linear distribution, and I highly doubt it being polynomial (although it could involve a root function).

Any help would be appreciated.

Thanks.
 
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How did you get the sequence?
 
The sequence is the set of n's where | ∑_{k=0}^{n} a_{k}z^{k} | is a local maximum in the sequence of the magnitudes of partial sums (the partial sums are complex valued).
 

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