Parasitic number, where does their name come from?

Question

Parasitic numbers, they are nice for recreational purposes, where I got notice of them (I found some of them by considering the solvability of a suitable diophantine equation). But, I couldn't figure, considering their definition and properties, why "parasitic" (what do they parasite? etc.)

Answer 1

It seems to have been invented by C. A. Pickover in his book "Wonders of Numbers". From this quirky site I was able to extract the following which I assume is from Chapter 80 of that book:

"Help! Get it off me," Monica screamed. Dr. Googol and Monica were exploring the deep jungles of Africa when she discovered a wet leech stuck to her ankle. Dr. Googol nodded, withdrew a salt shaker from his backpack, and sprinkled salt on the leech. It began to scream and promptly dropped to the moist forest floor. Monica took a deep breath. "Thank you." They resumed their hike as Dr. Googol told Monica all about parasites. The number 102,564 is a remarkable number that Dr. Googol discovered one day during his late-evening computer explorations. He calls this number a parasite number, for reasons that will soon become clear. In order to multiply 102,564 by 4, simply take the 4 off the right end and move it to the front to get the answer. In other words, the solution is the same as the multiplicand except that the number 4 on the right side is moved to the left end:

Isn't this an incredible number? How many numbers with this quality exist within the numerical jungle, swimming peacefully and undetected in the swamp of mathematics? These kinds of numbers remind Dr. Googol of a biological organism that contains a parasite (digit) that roams around the body of the host organism (the multidigit number in which the parasite resides) as it gains energy by feeding (the multiplication operation). Dr. Googol has written several programs to search for parasite-containing numbers (or parasite numbers, for brevity), such as 102,564. If you search for all potential parasite numbers generated by different 1-digit multipliers, you'll find that they are exceedingly rare. It seems that the only parasite number less than 1 million is the 4-parasite 102,564. (The term 4-parasite indicates that the number 4 is the multiplier.) Do the other digits give rise to any parasite numbers? Are there multipliers for which no parasite number exists? How much computer time will be spent on this, now that Dr. Googol has asked this question?

I admit the evidence is sketchy, but it does at least give an explanation for the term. The Wiki article also references "Wonders of Numbers", though it refers to chapter 28.