Fractional Series which approach the square roots of prime numbers.

duren99109
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Such as sqrt 5: (2.236067977...)
Start with the fractional seeds 2/1, 9/4,...

New members are generated (both numerators and denominators) by the rule new member = 4 times the current plus the previous.

Which generates the progrssion 2/1, 9/4, 38/17, 161/72, 682/305, 2889/1292, 12238/5473, 51841/23184... (and this process keeps generating the digits of the irrational root)

Have found the seeds and rules of production for the sqrts of primes 2 through 23 and trying to find patterns...

anybody either (1) know about this stuff, or (2) find it of interest?

I would appreciate any thoughts on the matter...
 
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You can look up continued fractions which are similar to what you describe.
 

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