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Search: id:A132660
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| A132660 |
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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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+0
1
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| 339542, 355877, 372554, 385263, 388943, 415683, 423413, 435267, 487386, 513728, 514377, 538271, 578979, 625958, 629721, 657971, 661977, 731618, 738792, 739278, 753921, 797454, 853892, 856529, 963458
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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EXAMPLE
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355877^2 = 126648439129.
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MATHEMATICA
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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
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CROSSREFS
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Sequence in context: A069337 A022225 A114674 this_sequence A103808 A029568 A015321
Adjacent sequences: A132657 A132658 A132659 this_sequence A132661 A132662 A132663
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KEYWORD
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base,fini,full,nonn
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AUTHOR
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Wei-Hwa Huang (onigame(AT)gmail.com), Nov 15 2007
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EXTENSIONS
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Many terms were wrong. Corrected by Zak Seidov, Nov 19 2007
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