OFFSET
1,1
COMMENTS
Also of note is the unique number 314, which together with its sixth power 958468597212736 has the property that each digit from 1 to 9 occurs exactly twice. Aside from trivial cases that use zeroth powers, these are all the cases where two numbers that are powers of the same base have this property. [Comment corrected by Tanya Khovanova, Dec 18 2007]
Found by exhaustive search.
EXAMPLE
355877^2 = 126648439129.
MATHEMATICA
Select[Range[1000000], Sort[Join[IntegerDigits[ # ], IntegerDigits[ #^2 ]]] == {1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9} & ] - Tanya Khovanova, Dec 18 2007
CROSSREFS
KEYWORD
base,fini,full,nonn
AUTHOR
Wei-Hwa Huang (onigame(AT)gmail.com), Nov 15 2007
EXTENSIONS
Many terms were wrong. Corrected by Zak Seidov, Nov 19 2007
STATUS
approved