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A174823
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Numbers n such that the union of the decimal digits of n^2 and n^3 contains every decimal digit exactly three times.
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0
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OFFSET
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1,1
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COMMENTS
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The sequence is finite (proof in reference). There are exactly 10 numbers.
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REFERENCES
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J.-M. De Koninck - Armel Mercier, 1001 problemes en theorie classique des nombres,
exercise number 255 p. 184, Ellipses, Paris 2004.
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LINKS
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Table of n, a(n) for n=1..10.
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EXAMPLE
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497375 is in the sequence because :
497375^2 = 247381890625 ; 497375^3 = 123041567849609375 ;
and the union of the digits is :{247381890625123041567849609375} contains 3 digits "0",
3 digits "1", 3 digits "2", ..., 3 digits "9".
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MAPLE
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with(numtheory): U:=array(1..30) :c:=0:for i from 300000 to 1000000 do: n2:=i^2:n3:=i^3:l2:=length(n2):l3:=length(n3):if l2=30-l3 then n0:=n2:nn0:=n3:for m from 1 to l2 do:q2:=n0:u2:=irem(q2, 10):v2:=iquo(q2, 10):n0:=v2 : U[m]:=u2:od:for mm from l2+1 to 30 do:q3:=nn0:u3:=irem(q3, 10):v3:=iquo(q3, 10):nn0:=v3 : U[mm]:=u3: od: s1:=0:s2:=0:s3:=0:for j from 1 to 30 do:s1:=s1+U[j]^3:s2:=s2+U[j]^7:od:if s1=6075 and s2=24241275 then c:=c+1:printf(`%d, `, i): else fi:else fi:od: print(c):
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CROSSREFS
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Sequence in context: A209856 A082248 A166196 * A145539 A157759 A187313
Adjacent sequences: A174820 A174821 A174822 * A174824 A174825 A174826
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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Michel Lagneau, Jan 01 2011
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STATUS
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approved
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