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Numbers which, together with their squares in base ten, contain all digits from 1 to 9 exactly twice.
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%I #2 Jun 29 2008 03:00:00

%S 339542,355877,372554,385263,388943,415683,423413,435267,487386,

%T 513728,514377,538271,578979,625958,629721,657971,661977,731618,

%U 738792,739278,753921,797454,853892,856529,963458

%N Numbers which, together with their squares in base ten, contain all digits from 1 to 9 exactly twice.

%C 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]

%C Found by exhaustive search.

%e 355877^2 = 126648439129.

%t 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

%K base,fini,full,nonn

%O 1,1

%A Wei-Hwa Huang (onigame(AT)gmail.com), Nov 15 2007

%E Many terms were wrong. Corrected by Zak Seidov, Nov 19 2007