A188545 Fusible numbers.

1, 3, 10

Offset: 0

Author

Ed Pegg Jr, Apr 03 2011

Keywords

• nonn
• hard
• bref

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.
• Ed Pegg Jr, YouTube: The Fuse Problem.
• Junyan Xu, Survey on Fusible Numbers, arXiv:1202.5614 [math.CO], 2012.

Crossrefs

Cf. A283075, A287012.