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A188545 Fusible numbers. 3
1, 3, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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
LINKS
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.
Junyan Xu, Survey on Fusible Numbers, arXiv:1202.5614 [math.CO], 2012.
CROSSREFS
Sequence in context: A057269 A113116 A137044 * A336747 A212361 A011998
KEYWORD
nonn,hard,bref
AUTHOR
Ed Pegg Jr, Apr 03 2011
STATUS
approved

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Last modified June 17 12:36 EDT 2024. Contains 373445 sequences. (Running on oeis4.)