A193345 Digits occurring in A173616.
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
Offset: 1
Examples
1111^1111=.........8711; 111^111=........711; 10^(1-4)(8711-711)=8 ==> a(4)=8 Comment from _Aswini Vaidyanathan_, May 11 2013: 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).
Programs
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Mathematica
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}] -
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)
Extensions
Edited by N. J. A. Sloane, May 12 2013
Comments