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A225458 10-adic integer x such that x^9 = 9.

%I A225458 #17 Aug 14 2019 08:32:35
%S A225458 9,8,2,1,2,9,8,0,2,7,6,9,1,4,4,8,0,3,4,5,3,6,1,1,9,4,4,9,6,7,2,0,3,1,
%T A225458 3,2,4,9,5,0,4,9,4,0,0,9,4,7,4,6,6,3,3,6,5,1,7,2,1,9,9,0,9,0,5,1,4,9,
%U A225458 6,5,5,5,1,2,7,7,0,2,0,6,2,2,2,6,1,5,9,5,0,1,8,0,6,8,1,2,3,6,7,1
%N A225458 10-adic integer x such that x^9 = 9.
%H A225458 Seiichi Manyama, <a href="/A225458/b225458.txt">Table of n, a(n) for n = 0..10000</a>
%F A225458 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + b(n-1)^9 - 9 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - _Seiichi Manyama_, Aug 14 2019
%e A225458        9^9 == 9 (mod 10).
%e A225458       89^9 == 9 (mod 10^2).
%e A225458      289^9 == 9 (mod 10^3).
%e A225458     1289^9 == 9 (mod 10^4).
%e A225458    21289^9 == 9 (mod 10^5).
%e A225458   921289^9 == 9 (mod 10^6).
%o A225458 (PARI) n=0;for(i=1,100,m=9;for(x=0,9,if(((n+(x*10^(i-1)))^9)%(10^i)==m,n=n+(x*10^(i-1));print1(x", ");break)))
%o A225458 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((9+O(2^N))^(1/9), 2^N), Mod((9+O(5^N))^(1/9), 5^N)))), N) \\ _Seiichi Manyama_, Aug 06 2019
%o A225458 (Ruby)
%o A225458 def A225458(n)
%o A225458   ary = [9]
%o A225458   a = 9
%o A225458   n.times{|i|
%o A225458     b = (a + a ** 9 - 9) % (10 ** (i + 2))
%o A225458     ary << (b - a) / (10 ** (i + 1))
%o A225458     a = b
%o A225458   }
%o A225458   ary
%o A225458 end
%o A225458 p A225458(100) # _Seiichi Manyama_, Aug 14 2019
%Y A225458 Digits of the k-adic integer (k-1)^(1/(k-1)): A309698 (k=4), A309699 (k=6), A309700 (k=8), this sequence (k=10).
%K A225458 nonn,base
%O A225458 0,1
%A A225458 _Aswini Vaidyanathan_, May 11 2013