|
|
A188545
|
|
Fusible numbers.
|
|
3
|
|
|
|
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
|
|
|
|