Super Safi’s Monday Morning Math Mayhem 23 – Smith Numbers

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

 

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

In honour of Canadian Thanksgiving on Monday October 14th, we go back to the first Thanksgiving episode of The Simpsons and look at Smith numbers.

 

In Bart vs. Thanksgiving (Season 02, Episode 07), Homer goes to pick up Abe from the Retirement Castle to bring him back for Thanksgiving dinner. We get a glimpse of Homer’s license plate.

While since The Simpsons Movie first originated it’s use, Homer’s car license plate has typically been seen as 1PHL07, on more than a dozen occasions. However, prior to the movie, his license plate varied, and included such plates as 3FJP24, KL5311, R8DMT, and 795DVI to name a few.

However, in Bart vs. Thanksgiving (Season 02, Episode 07), Homer’s plate is seen as 202VXX. Today, for Thanksgiving, we give thanks for Smith numbers, including 202.

 

Smith Numbers

A Smith number is a number for which the sum of its digits is equal to the sum of the digits in its prime factorization.

The sum of the digits of 202 are 4 (2 + 0 + 2). As the prime factorization of 202 is 2 x 101, the sum of the digits in the prime factorization of 202 are 4 (2 + 1 + 0 +1). Therefore 202 is considered a Smith number, as both the sum of its digits is equal to the sum of the digits in its prime factorization.

 

In the same Thanksgiving episode, Bart goes to donate blood to earn $12. The address for the Springfield Plasma Center is 2,416.

We can check and see if 2,416 is a Smith number.

The sum of the digits are 2 + 4 + 1 + 6 = 13.

The prime factorization of 2,416 is 2 x 2 x 2 x 2 x 151. The sum of the digits of the prime factorization are 2 + 2 + 2 + 2 + 1 + 5 + 1 = 15.

As the two values are not equal, 2,416 is not a Smith number.

 

The Smith numbers less than 1,000 are 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, and 985.

Yes, next weeks 666th episode, THOH XXX, will mark another Smith number this season; following the season premiere, which was episode 663.

 

Smith numbers were named by American mathematician Albert Wilansky of Lehigh University. He noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith.

The sum of the digits are 4 + 9 + 3 + 7 + 7 + 7 + 5 = 42.

The prime factorization of 4,937,775 is 3 × 5 × 5 × 65837. The sum of the digits of the prime factorization are 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42.

Albert Wilansky

 

Now that we’ve completed a look at Smith numbers, let’s give thanks for another mathematical wonder .

If you love math or enjoy reading these posts, don’t forget to stop by the Addicts Shop and check out all the paraphernalia, including the Math Mayhem shirts and hoodies.

Were you familiar with Smith numbers? Do you remember this Thanksgiving episode? Did you notice the license plate in this episode? Do you celebrate Thanksgiving? To all my fellow Canucks, happy Thanksgiving. Sound off in the comments below. You know we love hearing from you.

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40 responses to “Super Safi’s Monday Morning Math Mayhem 23 – Smith Numbers

  1. Interesting. It says a lot about the mind of a mathematician that this notion was even realized/discovered AT ALL. And tells even more that the FIRST example ever realized was 4,937,775 instead of 4…or 22. Dang.

    Liked by 1 person

  2. Is there an equation for Bart’s Law, showing that whether by investing in expansion or bonus, the greater the earning power of your Springfield then the higher the risk of the servers going into meltdown ?!! 😜

    Liked by 1 person

  3. Amazing

    Liked by 1 person

  4. Two reasons this post is awesome:
    A) I’d never heard of Smith numbers until just now
    2)That Mr. Wilanski named it after someone other than himself

    Also, for the record, the flavoring everything pumpkin every Fall is out of control! Pumpkin Coffee & Donuts at Dunkin’? Sacreligious!
    Twinkies? Nasty! Next they’ll be making pumpkin flavor Oreo’s … Thou shalt not mess with my Oreo flavors!!!
    ~MIB👤

    Liked by 2 people

  5. How come no update?

    Like

  6. Interesting, hadn’t heard of this before.

    Liked by 1 person

  7. Whoa, cool! Never heard of Smith numbers.
    Thanks a lot Safi! 👏

    Liked by 1 person

  8. This one here breaks my noodle… so am off to drawing.. Inktober anyone? if so, I have been posting my “art” in tweeter: k00lviruz 🙂

    Liked by 1 person

  9. Happy Thanksgiving! More turkey…less math.

    Liked by 1 person

  10. Similar to Homer’s “everything is ok alarm”, can we get a “there is still no THOH update” post every 5 to 10 minutes.

    As an aside, I think it would be ok if you set the frequency to be a Smith number.

    Liked by 2 people

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