Back in 1994 I guess I went a little crazy and started excessively playing with numbers. I even had a dream about them and started to think they were trying to tell me things. (Did I say crazy?) However, in Jan, of 1999 I was still ignorant enough to think I could discover a new constant. I mentioned that I even had one notable “number dream.” Close to the very end of 1998 I had a very vivid dream about the integers. It kind of led me to playing with roots of positive integers, looking for some type of curve that got “flatter and flatter.” The “sum function” really intrigued me at that time so I began to spend a good deal of my nervous energy playing with it. I began to reason that the only way the sum function was going to produce a graph that became flatter and flatter was to use an alternating series. I was familiar with them from when I wrote a couple of programs for my new calculator, a TI 92 a step up from my Casio grapher. The programs computed an arbitrary number of digits for sine and cosine. Since my TI 92 had a sum function I used it, the Inverse Symbolic Calculator and then a version of Mathcad, that I got real cheap, to experiment with alternating sums of the roots of integers. By Jan 11, 1999 I had a little expression that when calculated seem to give a result that converged. I began to think of the result of that computation as a constant. I first called the constant rc for root constant: see http://marvinrayburns.com/Original_MRB_Post.html.
I kept on writing people and posting messages, on Dave's math tables and Algebra online, about that constant. Here is another message, I started a few days later, http://math2.org/mmb/thread/901. One person I had previously wrote to a bit, about numeric computations involving logarithms I wanted to do on My TI 92, was Simon Plouffe. I knew he kept a table of constants on the Inverse Symbolic Calculator, so I blatantly told him that I discovered a new constant. I’m sure he took that with a grain of salt; nonetheless he told me that he would put it into his table of constants. He referred to it simply as Marvin Ray Burns’ constant. I assume he just meant, “The constant that Marvin mentioned.” When he republished his list of constants on http://pi.lacim.uqam.ca/eng/table_en.html, he called it the MRB constant.