6^6^6

The number $6^{6^{6}}$ is approximately 2.659119772153226 × 10³⁶³⁰⁵. The sequence $6^{6^{6}}\mod n$ starts out 0, 0, 0, 0, 1, 0, 1, 0, 0, 6 and can be computed in Mathematica by Table[PowerMod[6, 6^6, n], {n, 100}]. The sequence $9^{9^{9}}\mod n$ is A129810.