A group at RAIR lab at RPI is devoted to classifying candidate solutions for this function, and have made use of tree-normalization to do so.
A group at RAIR lab at RPI is devoted to classifying candidate solutions for this function, and have made use of tree-normalization to do so. Using up-arrow notation, Milton Greene showed that when k is the input to this function, it will be greater than "3 followed by point five k minus2 up arrows followed by 3." This function, which was introduced alongside the maximum shifts function, equals 6 for n = 3, 13 for n = 4, 4,098 for n = 5, but for n = 6, its current value is not known, but we know that it is greater than 3.5 times 10 to the 18,267th power. Represented with a sigma, it asymptotically grows faster than any computable function. This function was discussed in a paper fixing the number of states in a program's input, and it counts the number of1s outputted by a namesake device. For 10 points, identify this function created by Tibor Rado, which is named for a type of Turing machine that is itself named for a hard-working animal. 
A group at RAIR lab at RPI is devoted to classifying candidate solutions for this function, and have made use of tree-normalization to do so.
Busy Beaver function [do not accept or prompt on "beaver function"]