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%I #49 Aug 28 2021 09:54:48
%S 1,3,10
%N Fusible numbers.
%C Given irregular one minute fuses, the shortest amount of time that can be measured over n minutes is time(n) = n + 1/2^(fuse(n)) minutes. For example, fuse(1)=3, for 9/8 = 1 + 1/(2^fuse(1)). Over 2 minutes, time(2) = 2 + 1/(2^fuse(2)) = 2049/1024 minutes. The value for fuse(3) is larger than 2↑↑↑↑↑↑↑↑↑16, in Knuth's up-arrow notation. - _Ed Pegg Jr_, Apr 03 2011; edited by _Junyan Xu_, Jan 04 2012
%H Jeff Erickson, <a href="http://www.mathpuzzle.com/fusible.pdf">Fusible Numbers</a>, 2010. (Caution: some claims from these slides later turned out to be incorrect.)
%H Jeff Erickson, Gabriel Nivasch, Junyan Xu, <a href="https://doi.org/10.1109/LICS52264.2021.9470703">Fusible numbers and Peano Arithmetic</a>, 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS); arXiv:<a href="https://arxiv.org/abs/2003.14342">2003.14342</a> [cs.LO], 2020.
%H Ed Pegg Jr, <a href="http://www.youtube.com/watch?v=IDEXASbtknw">YouTube: The Fuse Problem</a>.
%H Junyan Xu, <a href="https://arxiv.org/abs/1202.5614">Survey on Fusible Numbers</a>, arXiv:1202.5614 [math.CO], 2012.
%Y Cf. A283075, A287012.
%K nonn,hard,bref
%O 0,2
%A _Ed Pegg Jr_, Apr 03 2011
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