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Two more sequences

  1. Feb 13, 2006 #1
    Just futzing around, this sequence was suprisingly patterned for the first 8 numbers, then became erratic:

    1, 1, 3, 3, 9, 9, 15, 15, 17, 27, ?

    And for the sake of more fooling around, this one just popped into my head:

    1, 2, 4, 6, 16, 18, 64, 66, 100, 112, ?

    DaveE
     
  2. jcsd
  3. Feb 16, 2006 #2
    Hm... perhaps hints are in order?

    Hint: Think primes!
    Hint: Think factors!
    (and you might not want to bother trying to find the next number in the sequence, if going by hand)


    DaveE
     
  4. Feb 18, 2006 #3
    is the second sequence something like:

    a(n) = the smallest number with n distinct factors (this would explain the odd-numbered terms being squares)

    havent looked at the first one yet, but the second jumped out at me
     
  5. Feb 18, 2006 #4
    Yep! Or, close enough. The smallest number with n distinct factors that's larger than a(n-1). Nice job! Now for the 1st one!

    DaveE
     
  6. Feb 18, 2006 #5

    siddharth

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    Is the first sequence:

    a(n) = 2* nth prime number - (n+1)th prime number ?
     
  7. Feb 21, 2006 #6
    Bingo!

    DaveE
     
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