Find three distinct positive integers p, q and r such that the value of expression 1/p+1/q+1/r will be less than 1/2 but as close to it as possible.

Find four distinct positive integers p, q, r and t such that the value of expression 1/p+1/q+1/r+1/t will be less than 1 but as close to it as possible.

The Online Encyclopedia of Integer Sequences entry A000058 identfies this sequence as Sylvester's sequence and extends it further: 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, 12864938683278671740537145998360961546653259485195807

 

Posted by Brian Smith on 2012-11-26 13:12:03