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A225455 10-adic integer x such that x^9 == (10^n-1)/9 mod 10^n for all n.

%I A225455 #8 Oct 04 2018 10:43:24
%S A225455 1,9,3,4,8,5,1,1,9,3,5,8,6,8,7,0,8,3,8,4,5,2,6,8,7,2,8,2,5,8,9,8,2,0,
%T A225455 5,0,8,7,4,3,6,6,9,4,4,3,6,2,2,8,0,2,2,3,7,5,2,0,5,5,6,9,2,8,2,7,1,7,
%U A225455 1,0,8,0,6,3,0,8,8,8,6,7,6,7,5,7,4,9,8,1,5,5,2,1,7,0,3,1,6,0,6,9
%N A225455 10-adic integer x such that x^9 == (10^n-1)/9 mod 10^n for all n.
%H A225455 Robert Israel, <a href="/A225455/b225455.txt">Table of n, a(n) for n = 1..10000</a>
%e A225455 1^9 == 1 (mod 10).
%e A225455 91^9 == 11 (mod 100).
%e A225455 391^9 == 111 (mod 1000).
%e A225455 4391^9 == 1111 (mod 10000).
%e A225455 84391^9 == 11111 (mod 100000).
%e A225455 584391^9 == 111111 (mod 1000000).
%p A225455 A[1]:= 1: P:= 1:
%p A225455 for d from 2 to 100 do
%p A225455   R:= (expand((10^(d-1)*x+P)^9 - ((10^d-1)/9)) mod 10^d)/10^(d-1);
%p A225455   A[d]:= subs(msolve(R,10),x);
%p A225455   P:= subs(10^(d-1)*A[d]+P);
%p A225455 od:
%p A225455 seq(A[i],i=1..100); # _Robert Israel_, Oct 03 2018
%o A225455 (PARI) n=0;for(i=1,100,m=(10^i-1)/9;for(x=0,9,if(((n+(x*10^(i-1)))^9)%(10^i)==m,n=n+(x*10^(i-1));print1(x", ");break)))
%K A225455 nonn,base
%O A225455 1,2
%A A225455 _Aswini Vaidyanathan_, May 11 2013