A Smith number is a composite number for which, the sum of its digits is equal to the sum of the digits in its prime factorization.
By definition, the factors are treated as digits.
For example, 22 =2*11 is a Smith numberbecause 2 + 2 = 2 + 1 + 1.
Another example: 666 = 2*3*3*37 and 6+6+6 = 2+3+3+(3+7 ).

The following table provides the least number of the 1st occurrence of K consecutive Smith numbersfor K=1, 2, 3, …

Please extend it as far as you are able to.

K ......First member of the least K-tuplet
1 ......4
2 ......728
3 ......73615**
4 .......FIND OUT
5 .......FIND OUT
6 +++ How far can you reach?


**Rem: The third number is 73615, since (73615, 73616, 73617) is the first example of 3 consecutive Smith numbers.
G o o d L u c k !

(In reply to re: 7-up by Ady TZIDON)

What is the mistake in using the multiplication symbol × ?

I realize that many programming languages and applications use the asterisk as the multiplication symbol and might reject the multiplication symbol × (Unicode x'00D7'), yet it was a choice in presentation. Is it failing to appear correctly in your browser?

Posted by Dej Mar on 2010-08-23 20:24:40