Joke number

Computer Science Level 4

Smith Numbers are composite numbers n n such that sum of digits of n = n= sum of digits of prime factors of n n (counted with multiplicity).

For example : 58 = 2 × 29 58=2 \times 29 and 5 + 8 = 2 + 2 + 9 = 13 5+8=2+2+9=13 . so 58 is a Smith number.

Find the first number n n such that n , n + 1 , n + 2 , n + 3 n,n+1,n+2,n+3 are smith numbers


The answer is 4463535.

Abdeslem Smahi by Abdeslem Smahi , 24, Algeria

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1 solution

Bill Bell
Jan 27, 2016 
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from sympy import factorint
from sortedcontainers import SortedList
import pyprimesieve

def isSmithNumber(n, show=False):
    if n in primes:
        return False
    v=factorint(n)
    left=sum(map(int,list(''.join([v[i]*str(i) for i in v])))) 
    right=sum(map(int,list(str(n))))
    if show:
        print v
        print map(int,list(''.join([v[i]*str(i) for i in v])))
        print map(int,list(str(n)))
    return left==right

primes=SortedList(pyprimesieve.primes(5000000))

n=0
count=0
while True:
    if isSmithNumber(n):
        count+=1
        if count==4:
            print n-3, isSmithNumber(n-3,True)
            break
    else:
        count=0
    n+=1

And very reassuring to find that my result agreed with what's available on oeis.org. :)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

my answer is coming out 17837.

gurdeep singh - 4 years ago

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