I've always wondered how some "mathematical coincidences" are published, or spread to a wider audience. For instance, the almost integer:


$$
e^\pi -\pi = 19.9990999\ldots
$$


was "*noticed almost simultaneously around 1988 by N. J. A. Sloane, J. H. Conway, and S. Plouffe*" ([Weisstein](http://mathworld.wolfram.com/AlmostInteger.html)). 


Were these "observations" published somewhere, and if so, what motivated such a publication, knowing that there was no explanation for the coincidence?



Publishing mathematical coincidences
You answered your question yourself: it is published on the web site that you refer to. The author of the web site cites his sources, in most cases these are personal communications. Many results of this sort are spread by correspondence, on Internet, and by oral personal communication. There is also a journal "[Experimental Mathematics](http://www.tandfonline.com/toc/uexm20/current)" which publishes these kinds of observations, even those for which the author has no explanation.


