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Math Help - A leading question: what do these numbers have in common?

  1. #16
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    Quote Originally Posted by wonderboy1953 View Post
    I believe it can be proven that no number larger than a three-digit number can be found
    with the desired properties.

    With larger numbers the number of combinations grows rapidly. So for a three-termed number, there are six combinations; when it's four termed, 24 combinations exist; five terms - 120 combinations and so on. It's already known that the primes thin out as they get bigger.

    The proof based on the aforementioned should be interesting if it hasn't been done yet.
    I was thinking similarly, but I don't think this constitutes a proof that such a set of numbers doesn't exist, merely that it is very very unlikely. Plus with a digit set like {1,1,1,1,1,1,1,1,1,1,3}, there are only 11 permutations instead of 11! because we are doing permutations of a multiset.
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    MathWorld has an extra prime repunit that is not listed on OEIS. So the sequence is 2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343, ... where 270343 isn't currently listed on OEIS. Looking closer: MathWorld says that the entries above 1031 are not proven but rather are just probable primes... this is mentioned in an OEIS comment but I'm surprised it is not mentioned in the main description; overall I find that format misleading.
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