I was curious to what would happen when you take a number, split it to its prime factors, add them up and then to repeat that sequence till you eventually get to a prime number. I was wondering what is the effect of this and what would happen the further you go up, I went up to one hundred and I think the higher you go the less likely 5 will be in the next number, as there are more and more primes. 4 is the only number which ends up to 4 and 5 is the first number the primes can go to, as 2 and 3 are to small because they can't be added with different primes. I know this may sound really confusing but I hope you understand. I'm just wondering if you have any information on this sequence? And is the pattern random or will you be able to know when the next number ends to 5 and the next ends to 13? This is what I've got (the first term being number 1):
1, 2, 3, 4, 5, 5, 7, 5, 5, 7, 11, 7, 13, 5, 5, 5, 17, 11, 19, 5, 7, 13, 23, 5, 7, 5, 7, 11, 29, 7, 31, 7, 5, 19, 7, 7
I think this sequence is interesting but I have no idea whether it's random or more numbers appear more than others further up you go. Since primes are rather random themselves does that make this sequence random too? What do you think?