The Fibonacci numbers are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

Fn = Fn-1 + Fn-2

with fixed values

F0 = 0 and F1 = 1.

The following example is an advanced implementation which combines Fibonacci series generation and searching next number for Fibonacci number which may or may not be in the Fibonacci series.

def fib_rec(n): if n == 1: return [0] elif n == 2: return [0,1] else: x = fib_rec(n-1) # the new element the sum of the last two elements x.append(sum(x[:-3:-1])) return x x=int(input("Enter the number of terms ")) result=fib_rec(x) print(result) n=int(input("enter any number from the above series")) c=0 a=1 b=1 if n==0 or n==1: print("Yes") else: while c<n: c=a+b b=a a=c if c==n: Next_number=n+1; print("next number is ",Next_number) else: print("Enter correct number")

The output of the program is

Rune-1: On correct input the out put is

Enter the number of terms 10

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

enter any number from the above series13

next number is 14

As I supplied number from series it will generate next number to that number that is not present in the list.

Rune-1: On Wrong input the out put is

Enter the number of terms 10

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

enter any number from the above series15

Enter correct number

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