Can you Identify a Pattern in this Sequence?

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In summary, the conversation discusses a sequence of numbers and the search for a recurrence relation to describe the pattern. While a possible pattern is identified, the conversation also mentions the difficulty in generating a recurrence relation for the sequence.
  • #1
FeDeX_LaTeX
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Hello;

Can you identify a pattern in this sequence of numbers (a recurrence relation)?

1, 3, 5, 9, 13, 17, 25, 33, 41, 49, 65, 81, 97, 113, 129, 161, 193, 225, 257, 289, 321, 385, 449, 513, 577, 641, 705, 769, 897, 1025, 1153, 1281, 1409, 1537, 1665, 1793, 2049, 2305, 2561, 2817, 3073, 3329, 3585, 3841, 4097, 4609, 5121, 5633...

I can sort of see a pattern but not a recurrence relation... if we look at how we can progressively get from term to term, it looks like this:

2¹ + 2¹ + 2² + 2² + 2² + 2³ + 2³ + 2³ + 2³...

So whenever you end up with a difference of 2n, you add that difference to any term n+1 times.

But generating a recurrence relation is more difficult...

Can you see a pattern?
 
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  • #2
http://www.research.att.com/~njas/sequences/A007664 [Broken]
 
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  • #3
Hi;

Yes, I have looked at this page before and done a google search for my sequence too... But I already know about the Frame-Stewart algorithm and that page lists findings already described in my post. But I was just wondering if anyone here was able to find a better pattern that connects all the terms, such that a recurrence relation can be formed and solved.
 

1. What is a pattern in a sequence?

A pattern in a sequence is a repeated or predictable sequence of numbers, symbols, or objects.

2. Why is it important to identify patterns in sequences?

Identifying patterns in sequences can help us understand and predict future events, solve problems, and make informed decisions.

3. How do you identify a pattern in a sequence?

To identify a pattern in a sequence, you can look for repeated numbers or symbols, observe the relationship between each element in the sequence, or try to find a mathematical rule or formula that describes the sequence.

4. Can patterns in sequences be random?

Yes, patterns in sequences can be random, especially in cases where the sequence is generated by a random process or does not follow a specific rule or formula.

5. Does every sequence have a pattern?

No, not all sequences have a pattern. Some sequences may appear random or have no discernible pattern, while others may follow a pattern that is difficult to identify.

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