My Math Forum Reverse Fibonacci series.

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 March 9th, 2019, 10:24 AM #1 Banned Camp   Joined: Nov 2018 From: Mumbai Posts: 32 Thanks: 1 Reverse Fibonacci series. Reference : https://www.programiz.com/c-programm...bonacci-series Can we write a computer program which will print reverse Fibonacci series numbers starting from 100 till 0? The computer program could be in any programming language viz C,C++,Java,C#, Python etc. Thanks & Regards, Prashant S Akerkar Last edited by akerkarprash; March 9th, 2019 at 10:25 AM. Reason: Content updates
March 9th, 2019, 10:34 AM   #2
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Quote:
 Originally Posted by akerkarprash Reference : https://www.programiz.com/c-programm...bonacci-series Can we write a computer program which will print reverse Fibonacci series numbers starting from 100 till 0? The computer program could be in any programming language viz C,C++,Java,C#, Python etc. Thanks & Regards, Prashant S Akerkar
Why are you asking these? Someone gave you a method of printing the numbers in a list backward in another thread. Are you actually asking about Fibonacci numbers rather than programming?

-Dan

 March 9th, 2019, 10:40 AM #3 Senior Member     Joined: Sep 2015 From: USA Posts: 2,550 Thanks: 1401 /* generate the Fibonacci series to a list or array */ a[1]=1;a[2]=1; for(i=3,i<=100,i++){ a[i]=[i-1]+a[i-2]; } /* read out the array backwards */ for (i=100,i>=1,i--) { printf("%d\n",a[i]); } That might be valid C (it's been decades) but it's better interpreted as pseudocode. Another method involves knowing $F_{100},~F_{99}$ ahead of time. Then you can do a[100]=$F_{100}$; a[99]=$F_{99}$; for (i=98,i>=1,i--){ a[i] = a[i+2]-a[i+1]; }
 March 9th, 2019, 10:41 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,968 Thanks: 2217 The number 100 isn't a Fibonacci number. It wasn't clear what was meant. However, individual Fibonacci numbers are easily calculated. Last edited by skipjack; March 9th, 2019 at 11:10 AM.
 March 9th, 2019, 10:44 AM #5 Banned Camp   Joined: Nov 2018 From: Mumbai Posts: 32 Thanks: 1 Thanks. https://www.programiz.com/c-programm...bonacci-series I want to trace the programming logic for printing the Fibonacci series in reverse order. Can we can term this new series as Reverse Fibonacci numbers series? Thanks & Regards, Prashant S Akerkar
 March 9th, 2019, 10:56 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,968 Thanks: 2217 Starting with which Fibonacci number? Fibonacci numbers can be quite large, so the languages you've mentioned might not be good choices.
 March 9th, 2019, 10:59 AM #7 Banned Camp   Joined: Nov 2018 From: Mumbai Posts: 32 Thanks: 1 Thanks. I feel we should start with 89 till 0 for printing Reverse Fibonacci numbers series. Next Fibonacci number after 89 is 144 which is greater than 100. Thanks & Regards, Prashant S Akerkar
 March 9th, 2019, 03:19 PM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Ye olde UBasic again: u=89 v=55 DOWHILE v>0 PRINT u, w=u-v u=v v=w ENDDO Output: 89,55,34,21,13,8,5,3,2,1,1 Thanks from topsquark
March 9th, 2019, 05:38 PM   #9
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Quote:
 Originally Posted by Denis Ye olde UBasic again: u=89
In order to find the right value of u you had to compute the Fibs forward. This is actually a harder and more interesting situation than the primes. How do you determine the largest Fib number less than some given value?

There turns out to be a closed-form expression for the n-th Fib, you could use that.

A Closed Form of the Fibonacci Sequence - Mathonline

 March 9th, 2019, 07:31 PM #10 Senior Member   Joined: Jun 2014 From: USA Posts: 564 Thanks: 43 If going back from 100, you could just write a sentence of the numbers as text... which I suppose is generally true of any finite initial segment written backwards. Calculating it isnâ€™t hard either as noted above. So long as your calculation of an initial and each successive Fib. is one that can be done in a finite number of steps, and in this case it most certainly is, there is a formula for it.

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