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Fractional Series which approach the square roots of prime numbers.

  1. May 4, 2004 #1
    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......
  2. jcsd
  3. May 4, 2004 #2


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    You can look up continued fractions which are similar to what you describe.
  4. Jun 18, 2004 #3
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