SOLUTION: What is the missing number in this pattern 5, 6, _, 19, 44, 93, _?

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Question 1146185: What is the missing number in this pattern 5, 6, _, 19, 44, 93, _?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
  5     6   ___    19    44    93   ___
     1   ___   ___    25    49   ___

Those differences are perfect squares.

     1²   ?²    ?²    5²    7²    ?²

Their square roots are
     
      1  ___   ___     5     7   ___


If we fill those blanks in with successive prime numbers,

      1    2     3     5     7    11

we have 1 together with the primes. 1 is neither prime nor
composite, and the primes are not composite.  So the sequence

      1    2    3      5     7    11

is the sequence of NON-COMPOSITE natural numbers.

So the differences are the successive squares of NON-COMPOSITE natural numbers,

      1²   2²   3²     5²    7²   11²
or
       1    4    9     25    49   121

So we fill in the missing differences and the missing terms:
 
    5     6    10    19    44     93   214
       1     4     9    25    49    121

Edwin