perplexus.info :: Sequences : Integers only

Integers only (Posted on 2014-03-31)

What is the smallest pair (a₁,a₂) of integers (a₁, less than a₂) to provide a list of 24 integers using
a recurrent function a_(n)=(a_(n-1)+a_(n-2))/2?

See The Solution Submitted by Ady TZIDON

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

re: Generalised approach

Comment 7 of 7 |

(In reply to Generalised approach by Harry)

Excellent finding, Harry!

I thought that your main points got buried, so I am reposting them. (No original work on my part was done)

You astutely wrote:

So for a₂₄ to be an integer, (a₂ – a₁) must be divisible by 2²²

If only positive integers are allowed for (a₁, a₂) then choose (1, 2²² + 1).

If zero is allowed then (0, 2²²) is best, as Jer recommended.

If all integers are allowed then (-2²¹, 2²¹) have the smallest abs. values

Posted by Steve Herman on 2014-04-01 08:53:55

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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info