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A188545
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Fusible numbers.
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3
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..2.
Jeff Erickson, Fusible Numbers, 2010. (Caution: some claims from these slides later turned out to be incorrect.)
Jeff Erickson, Gabriel Nivasch, Junyan Xu, Fusible numbers and Peano Arithmetic, 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS); arXiv:2003.14342 [cs.LO], 2020.
Ed Pegg Jr, YouTube: The Fuse Problem.
Junyan Xu, Survey on Fusible Numbers, arXiv:1202.5614 [math.CO], 2012.
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CROSSREFS
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Cf. A283075, A287012.
Sequence in context: A057269 A113116 A137044 * A336747 A212361 A011998
Adjacent sequences: A188542 A188543 A188544 * A188546 A188547 A188548
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KEYWORD
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nonn,hard,bref
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AUTHOR
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Ed Pegg Jr, Apr 03 2011
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STATUS
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approved
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