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12-digit Oddities

Math brain teasers require computations to solve.

 

Puzzle ID:#43854
Fun:*** (2.46)
Difficulty:**** (3.22)
Category:Math
Submitted By:javaguru*us**

 

 

 



What characteristic do these three 12-digit numbers share with each other, but with no other 12-digit number?

100307124369
111824028801
433800063225

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Comments

markmonninAus*
Jan 07, 2009

That's amazing trivia!
javaguru*us*
Jan 07, 2009

Thanks! I've never seen these before, but I was wondering if there were any that fit this pattern, so I wrote a program to find them.

Since then I submitted several series to the Online Encyclopedia of Integer Sequences (OEIS) about these numbers. (See http:// www.research.att.com/ ~njas/sequences/A153745.)
SweetiePi**
Feb 15, 2009

Wow. Cool!
Jimbo*au*
Mar 29, 2009

Very interesting but you surely aren't expecting us to get all of those properties without looking at the answer , are you?
javaguru*us*
Mar 29, 2009

I agree this is more of a puzzle than a teaser, but I think it's possible to get the answer. If you observe that the numbers are all squares and that their digital sums are all squares, I think it's possible to get the next step with the sum of the digit pairs.

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