Let us consider a sequence whose first term is 1.2 - and, the numbers appearing respectively to the right and the left of the decimal point of a given term are swapped and this number is added to a given term to obtain the next term.

For example, if a term is 46.78 then the next term will be 46.78+ 78.46 = 125.24.

For some of the terms in the sequence, the numbers appearing before the decimal point and the numbers appearing after the decimal point are congruent. Considering the first 30 terms, how many terms do have this property?

Note: Terms like 792.792 are deemed to have the desired property. However terms like 3870.387 do not possess this property as 3870 is not equal to 387.

(In reply to The easy way is turning out to be hard by Jer)

Silly me.  The display is 132385.3238 because it is only showing ten digits.  It is carrying more though.  The next digit is a 4 so it is correctly split into 132385 and .32384

The accuracy is then difficult to keep track of.

Still exploring.

Posted by Jer on 2011-11-16 12:05:31