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Formula Formulation (Posted on 2014-03-03) Difficulty: 3 of 5
A function f(N) is defined as:
f(1)=sod(12), f(2) = sod(122)
f(3) = sod(1212), f(4) = sod(12122), .... and, so on

Derive the general formula for f(N) in terms of N.

*** sod(x) denotes the sum of the digits of base ten expansion of x.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts first findings | Comment 2 of 4 |
The first 16 terms are 1,9,16,36,40,54,55,72,79,90,94,108,118,126,133,144

For even numbered terms after 2 it appears f(n)=9n, but I only checked up to 16.
For the odd numbered terms the answer is in the vicinity of 9n, but mostly under.  The differences (-8,-2,-2,-8,-2,-5,+1,-2) don't show any apparent pattern.
 
Edit: the pattern for evens breaks down at 20
f(20)=171 = 9*19

Edited on March 3, 2014, 4:29 pm
  Posted by Jer on 2014-03-03 16:26:12

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