User blog comment:Simply Beautiful Art/Slightly better upper bound to f 3 in the fgh/@comment-31663462-20180116133636/@comment-32783837-20180116195235

f3(2) = 2,048.

Since f2(n) = 2n×n,

f3(2)

= 2(2 2)×2 ×(22×2) = 28×8 = 256×8

= 2048

For f3(3), Hypercalc returns an approximation of 6.89508...×10121,210,694, and for f3(4), 1010 3.553934904655...×10 20.