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A193345
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Digits occurring in A173616.
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0
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1, 1, 7, 8, 7, 0, 1, 9, 7, 2, 3, 0, 8, 5, 5, 1, 9, 6, 5, 4, 6, 3, 8, 8, 0, 5, 5, 0, 3, 2, 7, 9, 6, 8, 6, 7, 5, 0, 4, 9, 5, 0, 5, 9, 9, 0, 5, 2, 5, 3, 3, 6, 6, 3, 4, 8, 2, 7, 8, 0, 0, 9, 0, 9, 4, 8, 5, 0, 3, 4, 4, 4, 8, 7, 2, 2, 9, 7, 9, 3, 7, 7, 7, 3, 8, 4
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OFFSET
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1,3
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COMMENTS
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This is the 10-adic integer x such that x^9 == (10^n-9) mod 10^n for all n. It is the 10's complement of A225458. - Aswini Vaidyanathan, May 11 2013
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LINKS
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EXAMPLE
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1111^1111=.........8711; 111^111=........711;
10^(1-4)(8711-711)=8 ==> a(4)=8
1^9 == 1 (mod 10).
11^9 == 91 (mod 100).
711^9 == 991 (mod 1000).
8711^9 == 9991 (mod 10000).
78711^9 == 99991 (mod 100000).
78711^9 == 999991 (mod 1000000).
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MATHEMATICA
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repunit[n_] := Sum[10^i, {i, 0, n-1}]; a[n_] := 10^(1-n)(PowerMod[repunit[n], repunit[n], 10^n] - PowerMod[repunit[n-1], repunit[n-1], 10^(n-1)]); Table[a[n], {n, 200}]
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PROG
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(PARI) n=0; for(i=1, 100, m=(10^i-9); for(x=0, 9, if(((n+(x*10^(i-1)))^9)%(10^i)==m, n=n+(x*10^(i-1)); print1(x", "); break))) (From Aswini Vaidyanathan, May 11 2013)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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