For some reason, I need them at my reach... Mostly to solve miscelleanous Math'n Code challenge using my languages of choice. Enjoy!
Hopefully they will be useful for somebody else
To calculate a(3) this how to proceed manually:
1: 3 ^ 3 mod 10 = 7
2: 3 ^ 7 mod 100 = 87
3: 3 ^ 87 mod 1_000 = 387
4: 3 ^ 387 mod 10_000 = 5_387
5: 3 ^ 5_387 mod 100_000 = 95_387
6: 3 ^ 95_387 mod 1_000_000 = 195_387
7: 3 ^ 195_387 mod 10_000_000 = 4_195_387
8: 3 ^ 4_195_387 mod 100_000_000 = 64_195_387
9: 3 ^ 64_195_387 mod 1_000_000_000 = 464_195_387
10: 3 ^ 464_195_387 mod 10_000_000_000 = 2_464_195_387
read a(3) = 2_464_195_387
namely aA165736(n) = n^(n^(n^(n^(n^(n^(n^(n^(n^(n^n mod 10) mod 100) mod 1_000) mod 10_000) mod 100_000) mod 1_000_000) mod 10_000_000) mod 100_000_000) mod 1_000_000_000) mod 10_000_000_000
Every implementation try to calculate the sequence using equivalent algorithm.