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Is The Year 2012 Special?


On Eric Friedman's List of special numbers, the number 2012 does not appear. In fact, as bookends, the numbers 2010 and 2015 are considered special because 2010 is the "number of trees on 15 vertices with diameter 7" and 2015 is a "a Lucas-Carmichael number." Thus, we apparently have a unspecial string for several more years!

But wait, I hear echoes of Bob Albrecht. There must be something special about the number 2012....

For example, 2012 = 4 x 503, where 4 is "smallest number of colors sufficient to color all planar maps" and 503 is the "smallest prime which is the sum of the cubes of the first 4 primes" (i.e. 503 = 23+3+5+7). And, it is the only number that fits that description.

Or, consider this equation, using the "floor" function and very special numbers...

Now that certainly makes 2012 special!

So, what is your task? Use your creativity to find other ways that 2012 is special? Use combinations of ideas such as the following...

  • Exponents
  • polygonal numbers (e.g. triangular)
  • Primes...twin primes, consecutive primes, emirps, etc.
  • Fibonacci and Lucas numbers
  • Perfect, Abundant, and Deficient numbers
  • Palindromes
  • Factorials
  • Exotic number types: Catalan, Motzkin, Kaprekar, Bell, Smith, etc.
  • Special functions: trig, logs, etc.
Share your results with me by e-mail so I can post them....

 

Source: B. Albrecht's "Happy New School Year!" Oregon Mathematics Teacher, Jan/Feb 2011, p. 21


Hint: Be creative...!

 


Solution Commentary: As I receive results, I will post them...