Does the md5 sum of the digits of a(42), followed by a single newline, come out to 686991ef31df3c46cdf8d1569782a78f I should have a(43) tonight, and in a few days, a(44). I'll check by calculating the residues modulo a few thousand moderate primes and compare that to what those residues should be. I could not find a bigint package that would do what I needed so I had to duct tape and baling wire together some code that keeps things within the limits of gmp. It's made more complicated by the fact that I don't have enough disk space for the intermediate results. Calculating the result in binary is actually pretty quick, but converting that result to decimal is challenging. On Tue, Nov 14, 2017 at 7:47 AM, Hans Havermann <gladhobo@bell.net> wrote:
Yesterday, Cliff Pickover's twitter feed presented a bit from Pickover's 2005 "A Passion for Mathematics" which references Guy's 1994 "Unsolved Problems in Number Theory" (2nd ed.) E15, a recursion of Göbel, wherein is stated that x(43) of the sequence is not an integer. The sequence is A003504:
There's a different offset in the OEIS version, so A003504(44) is now the first one that is not an integer. Pickover in his book felt the need to add something to the problem so, noting that A003504(44) = 5.4093*10^178485291567, he stated that this number "is so large that humanity will *never* be able to compute all of its digits".
I had a go on my four-year-old Mac Pro with 64 GB RAM and was only able to compute A003504(42) with its 44621322894 decimal digits. That suggests that when the next iteration of the Mac Pro, with 256 GB RAM, comes out in 2018 it should be able to calculate the number. But I know that there are personal computer setups out there right now that enjoy 256 GB RAM, so I emailed Cliff with a "never is now". :)
I'm curious to find out what the fractional part of the number will turn out to be. I think it'll be some integer divided by 43. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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