Marvin Ray Burns

 I've been using Maple since 1997 or so.

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These are Posts that have been published by Marvin Ray Burns

I define a partial repeating decimal as shown in the following example: if you have the decimal expansion 0.1728394877777777777777777777771939374652819101093837... 7 is called a partial repeating decimal.  

Back in 2000 I noticed a pattern in the decimal expansions of sin(10^-n) for growing n. Here is table of some integer n:

n                sin(10^-n)

1 9.98334166*10^-2

Back in 2000 I published A034948A036663, and A036664 in Sloane's Integer Sequences, now OEIS.

But today I decided to find the exact values of some such quotients.



Let d be the Feigenbaum delta constant 4.66920160910299067185320382046620161..., a be the Feigenbaum alpha constant 2.50290787509589282228390287321821578... and m be the MRB constant 0.18785964246206712024851793405427323....

d*m - 2 (600 a - 2537)/(5 a - 2373) = 9.232940534412995...*10^-19

or you could write

1/10*(d*m + 564446/(2373 - 5 a)) - 24 = 9.232940534412995...*10^-20

I've been playing around with power towers and thought my latest might be interesting enough to post.

I used Wolfram Alpha on the big numbers (n=5..50). Some corrected.

On May 17, 2013 I finished a 2,000,000 or more digit computation of the MRB constant, using only around 10GB of RAM. It took 37 days 5 hours 6 minutes 47.1870579 seconds. You can write for the digits.
The program I used was based on Richard E. Crandall's work:
Richard E. Crandall,Unified algorithms for polylogarithm, L-series, and zeta variants(53 pages)

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