Pattern | Fibonacci Num3ers- sum of square of digits is not 89

 
The first few Fibonacci numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, …

 

0^2   =   0
1^2   =   1
1^2   =   1

Fibonacci 3

Fibonacci 4

 

We also reach the number 89 with the next numbers in the series:
21,   34,   55,   89,   144,   233,   377,   610,   987,   1597

 
 
 
We don’t reach 89 with these pairs and triplet :

Fibonacci 1

Fibonacci 2

There are many Fibonacci numbers that don’t reach 89.
It’s interesting to find the peculiar ones, such as
pairs, triplets, quadruplets of consecutive Fibonacci numbers that don’t reach 89.

 
Check out:

Unhappy Number
http://mathworld.wolfram.com/UnhappyNumber.html

Happy Number
http://mathworld.wolfram.com/HappyNumber.html

 
 
 
 
 
 
   

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Math Beauty and tagged , . Bookmark the permalink.

6 Responses to Pattern | Fibonacci Num3ers- sum of square of digits is not 89

  1. Paul says:

    I’m reckoning there is some proof lurking in there, but on a brute force method I looked up to (Fn100000), some 20899 digits and those were the only 2 numbers to be found, what was surprising was even at that number of digits there wasn’t one that went over 12 iterations.
    considering that 987 has 10 iterations. (Fn100000) terminates after 7 iterations.
    Paul.

  2. Paul says:

    When I mentioned the only 2 numbers I meant 1 and 89 as they were the 2 numbers mentioned in the examples shown. I didn’t look for pairs of or triples of the number 1 but I did notice quite a few. I will take another look and look for some runs.

    Paul.

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