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A075309
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Distinct-digit perfect powers.
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6
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1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 125, 128, 169, 196, 216, 243, 256, 289, 324, 361, 512, 529, 576, 625, 729, 784, 841, 961, 1024, 1089, 1296, 1369, 1728, 1764, 1849, 1936, 2048, 2187, 2197, 2304, 2401, 2601, 2704, 2809, 2916, 3025, 3125, 3249, 3481
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Of 1110 perfect powers < 1000000, 259 are distinct-digit.
Sequence is finite. What is the index of the last term? Note that 2^30 = 1073741824, hence the highest power that occurs < 30. The frequency chart of a power r, 2 < r < 30 may be of some interest and could be included. - Amarnath Murthy, Dec 06 2003
There are a total of 657 distinct terms, the last of which is 99066^2=9814072356. The highest power occurs in 2^29. There are 609 squares, 39 cubes, 19 fourth powers, 9 fifth powers, 4 sixth powers, 4 seventh powers, 3 eighth powers, 2 ninth powers, 2 tenth powers and one each of powers 11, 12, 13, 14, 15, 20 and 29. These counts to not add to 657 because 1 is not counted and some powers, such as 2^4 = 4^2 = 16, are counted twice. - T. D. Noe, Aug 09 2005
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LINKS
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EXAMPLE
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100,121,144,343 etc. are not members.
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MAPLE
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lim:=floor(sqrt(9876543210)): A075309:={1}: for n from 2 to lim do k:=2: p:=n^k: while p<=9876543210 do p:=n^k: pandig:=true: d:=convert(p, base, 10): for j from 0 to 9 do if(numboccur(j, d)>1)then pandig:=false: break: fi: od: if(pandig)then A075309 := A075309 union {p}: fi: k:=k+1: od: od: op(sort(convert(A075309, list))); # Nathaniel Johnston, Jun 23 2011
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MATHEMATICA
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lst={1}; Do[k=1; While[k++; n=k^pow; n<10^10, d=IntegerDigits[n]; If[Length[Union[d]]==Length[d], AppendTo[lst, n]]], {pow, 2, 29}]; lst=Union[lst] (* T. D. Noe *)
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CROSSREFS
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KEYWORD
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easy,nonn,base,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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