|The protagonist in the latest novel by Jason Earls spends his time hunting down the evil and semi-mystical artist Zelian, and much of his spare time finding integers with interesting aesthetic and number theoretic properties. I'm supposing that Earls himself is not an adventurer trying to save the world from an evil artist, but it seems that he really does enjoy finding numbers with unusual properties.
I don't think that this can be considered ``math research'' in any way. Rather, it seems to be a form of artistic expression through mathematics. (And this is exactly how it is presented in the story.) Many of the numbers presented in the story are interesting in part because they are prime and because they create a recognizable image when laid out in a rectangular array. Some spell out words, some look like a man wearing a hat, and one particularly important one looks like the face of Zelian himself. Other properties of interest to Earls are religious significances (he uses 666 in the decimal expansion of a prime which spells out words like `holy' when put in an appropriate grid), being a triangle number (i.e. of the form n*(n+1)/2), having an even (or odd) number of 1's in the binary representation, and remaining prime when the digits are reversed. So, for instance, he begins to list the primes which remain prime when reversed and have an odd number of 1's in their decimal expansion.
The character in Cocoon of Terror also seems to reveal some of the techniques that Earls himself must use to find these numbers when he discusses the particular mathematical techniques used to identify a particular number as being prime.
I'm afraid I do not have much appreciation for this particular art form. (I do find beauty in mathematics, but my taste runs towards an appreciation for stunning theorems with the ability to make sense out of the chaos rather than properties of individual numbers.) However, if you share the author's fascination with properties of integers and enjoy mind-bending science fiction stories, you should give Cocoon of Terror a chance...and write to me with your own comments/ratings of it after you do!