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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

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.

CROSSREFS

Cf. A283075, A287012.

Sequence in context: A057269 A113116 A137044 * A336747 A212361 A011998

Adjacent sequences:  A188542 A188543 A188544 * A188546 A188547 A188548

KEYWORD

nonn,hard,bref

AUTHOR

Ed Pegg Jr, Apr 03 2011

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)