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User:Robert Munafo

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I am a maths hobbyist with a strong computer programming background.

Just after learning addition and multiplication "tables" (A3056 and A4247) in school I decided to take the process one step further and learned all values of Z = XY for X=2,3,5,6,7,11 and Z < 105. I spent much time over the next few years working on iterated exponentiation x\#y = ((x^{x})^{x . . .})^{x} = x^{x^{(y-1)}}, and solving things like xy = yx over the reals and over the rational numbers. I also wrote arbitrary-precision calculation libraries several times (first on an Apple II). During this early period my favorite sequence was probably A1146 (which I still know by memory up to the 264 term). My main focus on things that grow at an increasing rate (like A0108 and A6888) encouraged my interest in other types of maths, such as polyominoes (I verified that A0162(5) = 29 with only pen and paper).

I read much of Sloane's first book at age 14 and started collecting sequences on my own; I got my own copy in 1989 and began contributing in the early 1990's (beginning with most of A6874-A6888). Many of these early sequences are still only written in my copy of H.I.S., but you'll find a lot of them at some integer sequences.

I sometimes use sequences as an excuse to practice implementing algorithms that use many CPU cores in parallel. It humbles me somewhat to realize that a result that would have taken hours to get on the Apple II can now be done 16 times in parallel in under a millisecond.

In order to create a webpage on sequences that can be easily generated by recurrence relations, I developed a system for converting back and forth between a unique recurrence definition and a unique sequence number that completely encodes the information in the formula. See MCS. A related programming project is RIES, an expression-search for real-valued quantities that (for me) fills the niche of Plouffe's Inverter. As with successive approximations given by Continued_fractions, the RIES algorithm emits results whose accuracy and Kolmogorov complexity both surpass the preceding result. In other words, RIES gives the simplest, crudest approximation first, then proceeds through progressively more complex equations whose roots give progressively closer approximations.

My "Sloandora" project is an automated recommendation browser for OEIS sequences based on using cognitive mapping to identify OEIS data that is likely to be of interest to the user based on their "ratings" given to previously recommended sequences. The name is a reference to the Pandora music system, which inspired the idea for the interface. Sloandora is an effective use of parallel processing hardware: rating a single OEIS record requires a full-text correlation metric between the sequence and the entire rest of the OEIS (typically about 2 * 1011 individual comparisons) which takes a few seconds on a 16-processor system.

Presently, a Google search on "Large Numbers" turns up my page as the 4th result. "Munafo" combined with "numbers" or "sequences" will turn up more of my work.

Robert Munafo 18:22, 28 January 2013 (UTC)
Edited, Robert Munafo 21:15, 6 August 2016 (UTC)

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