Two more "never" examples from my youth ... "What's the largest number expressible with three digits?" I think this was meant to be without additional arithmetic signs, since 999!!!!... is unbounded with an arbitrary number of !s. It was probably intended as a trick puzzle, with the wrong answer being 999. The answer given is 9^(9^9), which has around 300M digits, and can be written sign-free with superscripts. At the time, this was too big to compute as a decimal digit string. [Using 1s, 2s, or 3s, and four or more digits makes a more interesting puzzle.] The second example is the "Cattle Problem of Archimedes", where the answer is 8 numbers of 100K+ digits. The account I read reported that there was a club (in New Jersey? c. 1900?) that computed a few dozen digits, high & low order. Math Comp used to publish reviews of math tables contributed to a repository (UMT, unpublished math tables). ~1970, someone contributed a solution to the cattle problem. Dan Shanks wrote a review, remarking that the contributor hadn't really solved the problem, since he had "only computed the number of Bulls", leaving 7/8 of the problem unfinished. Rich -----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Hans Havermann Sent: Tuesday, November 14, 2017 8:47 AM To: math-fun <math-fun@mailman.xmission.com> Subject: [EXTERNAL] [math-fun] Never so soon 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: http://oeis.org/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