6^2 - 5^2, 56^2 - 55^2, 556^2 - 555^2

6^2 - 5^2 = 11

Base-2 = 1011 ...Base-3 = 102 ... Base-4 = 23 ... Base-5 = 21 ...
Base-6 = 15 ... Base-7 = 14 ... Base-8 = 13 ... Base-9 = 12 ... Base-11 = 10

56^2 - 55^2 = 111

Base-2 = 1101111 ... Base-3 = 11010 ... Base-4 = 1233 ... Base-5 = 421
Base-6 = 303 ... Base-7 = 216 ... Base-8 = 157 ... Base-9 = 133

556^2 - 555^2 = 1111

Base-2 = 10001010111 ... Base-3 = 1112011 ... Base-4 = 101113 ... Base-5 = 13421
Base-6 = 5051 ... Base-7 = 3145 ... Base-8 = 2127 ... Base-9 = 1464

5556^2 - 5555^2 = 11111

Base-2 = 10101101100111 ... Base-3 = 120020112 ... Base-4 = 2231213 ...

Base-5 = 323421 ... Base-6 = 123235 ... Base-7 = 44252 ... Base-8 = 25547 ...

Base-9 = 16215

55556^2 - 55555^2 = 111111

Base-2 = 11011001000000111 ... Base-3 = 12122102020 ... Base-4 = 123020013
Base-5 = 12023421 ... Base-6 = 2214223 ... Base-7 = 641640 ... Base-8 = 331007
Base-9 = 178366

555556^2 - 555555^2 = 1111111

Base-2 = 100001111010001000111 ... Base-3 = 2002110011021 ... Base-4 = 10033101013

Base-5 = 241023421 ... Base-6 = 35452011 ... Base-7 = 12305251 ... Base-8 = 4172107
Base-9 = 2073137