Programa de Python para el enésimo múltiplo de un número en la serie de Fibonacci

Dados dos enteros n y k. Encuentre la posición del n\’ésimo múltiplo de K en la serie de Fibonacci.  
Ejemplos:

Input : k = 2, n = 3
Output : 9
3\'rd multiple of 2 in Fibonacci Series is 34 
which appears at position 9.

Input  : k = 4, n = 5 
Output : 30
5\'th multiple of 5 in Fibonacci Series is 832040 
which appears at position 30.

Una solución eficiente se basa en la siguiente propiedad interesante. 
La serie de Fibonacci siempre es periódica bajo representación modular. A continuación se muestran ejemplos. 
 

F (mod 2) = 1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,
            1,1,0,1,1,0,1,1,0,1,1,0,1,1,0 
Here 0 is repeating at every 3rd index and 
the cycle repeats at every 3rd index. 

F (mod 3) = 1,1,2,0,2,2,1,0,1,1,2,0,2,2,1,0
            ,1,1,2,0,2,2,1,0,1,1,2,0,2,2
Here 0 is repeating at every 4th index and 
the cycle repeats at every 8th index.

F (mod 4) = 1,1,2,3,1,0,1,1,2,3,1,0,1,1,2,3,
           1,0,1,1,2,3,1,0,1,1,2,3,1,0 
Here 0 is repeating at every 6th index and 
the cycle repeats at every 6th index.

F (mod 5) = 1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,
            2,2,4,1,0,1,1,2,3,0,3,3,1,4,0
Here 0 is repeating at every 5th index and
the cycle repeats at every 20th index.

F (mod 6) = 1,1,2,3,5,2,1,3,4,1,5,0,5,5,4,
            3,1,4,5,3,2,5,1,0,1,1,2,3,5,2
Here 0 is repeating at every 12th index and 
the cycle repeats at every 24th index.

F (mod 7) = 1,1,2,3,5,1,6,0,6,6,5,4,2,6,1,
            0,1,1,2,3,5,1,6,0,6,6,5,4,2,6 
Here 0 is repeating at every 8th index and 
the cycle repeats at every 16th index.

F (mod 8) = 1,1,2,3,5,0,5,5,2,7,1,0,1,1,2,
            3,5,0,5,5,2,7,1,0,1,1,2,3,5,0 
Here 0 is repeating at every 6th index and 
the cycle repeats at every 12th index.

F (mod 9) = 1,1,2,3,5,8,4,3,7,1,8,0,8,8,7,
            6,4,1,5,6,2,8,1,0,1,1,2,3,5,8 
Here 0 is repeating at every 12th index and 
the cycle repeats at every 24th index.

F (mod 10) = 1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,
             7,7,4,1,5,6,1,7,8,5,3,8,1,9,0.
Here 0 is repeating at every 15th index and
the cycle repeats at every 60th index.

Python3

# Python Program to find position of n\'th multiple
# of a number k in Fibonacci Series
 
def findPosition(k, n):
    f1 = 0
    f2 = 1
    i =2;
    while i!=0:
        f3 = f1 + f2;
        f1 = f2;
        f2 = f3;
 
        if f2%k == 0:
            return n*i
 
        i+=1
         
    return
 
 
# Multiple no.
n = 5;
# Number of whose multiple we are finding
k = 4;
 
print("Position of n\'th multiple of k in"
                "Fibonacci Series is", findPosition(k,n));
 
# Code contributed by Mohit Gupta_OMG

Producción: 
 

Position of n'th multiple of k inFibonacci Series is 30

Consulte el artículo completo sobre el enésimo múltiplo de un número en la serie de Fibonacci para obtener más detalles.
 

Publicación traducida automáticamente

Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA

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