# Determining a formula for a (sub)sequence

• smize
In summary, the conversation is about finding a formula for a non-finite sub-sequence of a sequence of natural numbers. The speaker has already determined that the sequence is not linear and is doubtful that it is polynomial, but it may involve a root function. They are seeking help and explain that the sequence is based on the magnitudes of partial sums of a complex-valued sequence.
smize
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.

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).

## 1. What is a (sub)sequence?

A (sub)sequence is a group of numbers or elements that are ordered and follow a specific pattern within a larger sequence.

## 2. How do you determine a formula for a (sub)sequence?

To determine a formula for a (sub)sequence, you need to first analyze the pattern of the numbers or elements in the sequence. Look for any repeated operations or changes in values. Then, use algebraic methods such as substitution and solving equations to find the formula.

## 3. What is the importance of finding a formula for a (sub)sequence?

Finding a formula for a (sub)sequence can help predict future terms in the sequence and provide a better understanding of the pattern and behavior of the sequence. This can also be useful in various fields such as mathematics, physics, and computer science.

## 4. Are there any specific techniques or strategies for determining a formula for a (sub)sequence?

There are various techniques and strategies for determining a formula for a (sub)sequence, such as using the difference or ratio method, looking for geometric or arithmetic patterns, and using algebraic manipulation. It is important to try different methods and find the one that works best for a particular sequence.

## 5. Can a formula for a (sub)sequence be wrong?

Yes, a formula for a (sub)sequence can be incorrect if there are errors in the analysis or if the sequence does not follow a specific pattern. It is important to check the formula by plugging in different values and seeing if it produces the correct results before using it for predictions or further calculations.

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