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 Quite a Smithonian! (Posted on 2010-08-21)
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 !

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: 7-up | Comment 5 of 8 |
(In reply to 7-up by Dej Mar)

Still many mistakes:

2*3+7+(1+3)

728 : 1st number of 1st Smith Brothers
7+2+8 =SHOULD BE
2*3+7+(1+3)

7+2+9 =SHOULD BE
3*6
....And many others

or

erase  the sums,

s

 Posted by Ady TZIDON on 2010-08-23 12:31:47

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