All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Function Function Function Function Foray (Posted on 2015-03-31) Difficulty: 3 of 5
N is a positive integer and F(N) denotes the sum of the base ten digits of N.

Find F(F(F(22016))) and F(F(F(F(22016))))

*** As an extra challenge, solve the puzzle without using a computer program assisted method.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution A good guess / computer help | Comment 1 of 2
The process of repeatedly applying F eventually gives the digital root of 2^2016.  
Powers of 2 have digital roots in a cycle of length 6.  2016 is divisible by 6 so the digital root of 2^2016 = the digital root of 2^0 = 1.
The question is then whether F has been applied enough times.

F(2^2016) should have be about 4.5*2016*log(2) = 2731.
F(F(2^2016)) will be a two digit number [unless F(2^2016) happens to be a power of 10]
F(F(F(2^2016))) will be 10
F(F(F(F(2^2016)))) will be 1.

Checking
https://oeis.org/A001370/b001370.txt
gives 
F(2^2016) = 2656
F(F(2^2016)) = 19
F(F(F(2^2016))) = 10
F(F(F(F(2^2016)))) = 1

  Posted by Jer on 2015-03-31 12:50:47
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information