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I know there is no repeatable pattern of digits but is there anything that precludes other patterns such as the above?

tex

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- Thread starter thetexan
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- #1

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I know there is no repeatable pattern of digits but is there anything that precludes other patterns such as the above?

tex

- #2

ProfuselyQuarky

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mfb

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No. It is expected that no such pattern exists ("normal number"), and billions to trillions of digits have been analyzed to look for patterns (for a huge amount of things you could call "pattern"), but there is no proof that no such pattern exists.Has anyone every discovered any patterns in pi such as...every 97th digit is a 3? or something similar?

There are irrational numbers with patterns like the one described by thetexan.

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ProfuselyQuarky

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You are right.There are irrational numbers with patterns like the one described by thetexan.

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Let's say they did find a pattern in an irrational number...every 105th digit is a 7. What would that imply? Would it still be irrational? Would we be able to figure out why the pattern exists?

tex

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fresh_42

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If we include a 7 at every 107th digit of ##\pi## I would bet the new number will still be transcendental. There are still 106 digits where anything can happen.

Let's say they did find a pattern in an irrational number...every 105th digit is a 7. What would that imply? Would it still be irrational? Would we be able to figure out why the pattern exists?

tex

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mfb

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As an example, if you replace every 105th digit in the decimal expansion of pi by 7, you get an irrational number with that pattern.

What does "why" even mean? Why is pi larger than 3?Would we be able to figure out why the pattern exists?

It would be

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