7
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These two separate sequences use the same rule and stop at the 13th term.

2, 1, 8, 5, 2, 5, 8, 6, 7, 9, 7, 7, 0

3, 1, 5, 3, 9, 2, 4, 3, 9, 7, 3, 1, 0

These examples are produced when the rule is applied to notable mathematical 'objects'. Other examples, using the same rule, are often shorter, but may be infinite. What are they based on?

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  • $\begingroup$ Is Rot13(zbqhyne qvivfvba) involved at all or am I completely on the wrong track? $\endgroup$ – Brandon_J Jan 21 at 18:29
  • $\begingroup$ @Brandon_J, it's a different track, and one which can be easily followed. $\endgroup$ – Tom Jan 21 at 18:33
  • $\begingroup$ The two given sequences stop at the 13th term. Other examples, with the same simple rule, can be infinite. $\endgroup$ – Tom Jan 21 at 20:40
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This is an interesting one, but the rule seems to apply to

Decimal expansions of numbers

The rule itself

starts at the first number, and then takes the number x farther down the line, where x is the current number. For example, if the number were 1.2345670 it would do 1, then 2 (one later) then 4 (2 later) then 0 (4 later) at which point it would end because there is no "zero later"

The particular sequences here are

e = 2.7182818284590452353602874713526624977572470936999595749669676277240753...

and

pi = 3.141592653589793238462643383279502884197169399375105820974...

An example of an infinite sequence would be

10/9 = 1.111111111...

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