I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless.

My idea is to amend my article with some theories that seemed useless when they are created but found use after some time.

I came with some ideas like the Turing machine but I think I'm not grasping the right examples. 

Can someone point me some theories that seemed like the Lychrel numbers and then become 'useful'?

Edit: As some people pointed out that I've published this on MSE I present a code here to find some candidates as Lychrel numbers. 

def reverseNum(n):
    st = str(n)
    return int("".join([st[i] for i in xrange(len(st)-1,-1,-1)]))

def isPalindrome (n):
    st = str(n)
    rev = str(reverseNum(st))
    return st==rev

def isLychrel (n, num_interations):
    p = n
    for i in xrange(num_interations):
            if isPalindrome(p):
                    return i
            p = p + reverseNum(p)
    return -1


for i in xrange(1000):
    p = isLychrel(i,100)
    if (p < 0):
            print i,p


Number theory, in particular investigations related to prime numbers, was famously considered useless (e.g., by Hardy) for practical matters. Now, since "everybody" needs some cryptography it is quite useful to know how to generate primes (e.g., for an RSA key) and alike, sometimes involving prior 'useless' number theory results.