Keith Number

KEITH NUMBER

Before  moving on to code let us talk about what is Keith number . A number is said to be Keith Number, if  it appears in the sequence where first n numbers are digits of  number itself and rest are formed by repeatedly adding the previous n numbers of the sequence . It is illustrated in the example below:

eg. 

1. 14 is a Keith number    

    Sequence formed by 14 is  1, 4, 5, 9, 14, . . . . 

    First two numbers(1, 4) are digits of number(14)  itself and rest are formed by adding the  previous  two numbers of sequence(1+4=5, 5+4=9, 9+5=14). 

2. 197 is a Keith number

    Sequence formed by 197 is 1, 9, 7, 17,  33,  57, 107, 197, . . . .

    First three numbers(1, 9, 7) are digits of number(197)  itself and rest are formed by adding the  previous  two numbers of sequence(1+9+7=17, 9+7+17=33, 7+17+33=57 ,17+33+57=107 , 33+57+107-=197). 

NOTE:t is recommended that you first try this question by yourself.

Python Code

# Program to check for  keith number

t=int(input("Enter the number of times you want to execute the program "))
#This loop is for the number of  times you want to execute the program.. You don't have to restart the program again and again
for _ in range(t):
    n=input("Enter a number to be checked for a Keith number ")
    length=len(n)
    lst=[]
    # Appending the digits of number to a list
    for i in n:
        lst.append(int(i))


    sum=0
    c=0

    # We will break the loop when  sum of the last n numbers of seequence will be greater than n itself
    while sum<int(n):
        #There is no  keith number from 1 to 10
        if int(n)>=0 and int(n)<=10:
            break

        # Adding the last n numbers from the sequence
        sum=0
        for i in range(len(lst),len(lst)-length,-1):
            sum+=lst[i-1]
        lst.append(sum)

        # If sum is equal to n then break the loop and initialize c to 1
        if sum==int(n):
            c=1
            break
    if c==1:
        print(f"{n} is a Keith number")
    else:
        print(f"{n} is a not Keith number")

Output:

Enter the number of times you want to execute the program 6

Enter a number to be checked for a Keith number 14

14 is a Keith number

Enter a number to be checked for a Keith number 12

12 is a not Keith number

Enter a number to be checked for a Keith number 5752090994058710841670361653731519

5752090994058710841670361653731519 is a Keith number

Enter a number to be checked for a Keith number 197

197 is a Keith number

Enter a number to be checked for a Keith number 47

47 is a Keith number

Enter a number to be checked for a Keith number 565

565 is a not Keith number

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