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A225452 Digits of the 10-adic integer (1/9)^(1/7). 4

%I #32 Aug 08 2019 10:07:18

%S 9,6,9,8,0,8,1,2,6,9,7,5,6,7,4,1,6,7,5,2,5,5,3,4,3,0,2,7,4,2,2,5,1,5,

%T 5,9,1,5,8,6,8,0,1,6,8,2,2,1,5,7,9,3,0,3,1,3,3,9,9,8,2,9,0,1,1,3,3,9,

%U 2,7,8,6,6,4,0,2,6,6,2,6,0,5,4,5,4,7,6,2,3,2,6,4,4,6,2,2,6,6,2,6

%N Digits of the 10-adic integer (1/9)^(1/7).

%C This is the 10's complement of A225443.

%H Seiichi Manyama, <a href="/A225452/b225452.txt">Table of n, a(n) for n = 0..10000</a>

%e 9^7 == -1 (mod 10).

%e 69^7 == -11 (mod 10^2).

%e 969^7 == -111 (mod 10^3).

%e 8969^7 == -1111 (mod 10^4).

%e 8969^7 == -11111 (mod 10^5).

%e 808969^7 == -111111 (mod 10^6).

%o (PARI) n=0;for(i=1,100,m=(8*(10^i-1)/9)+1;for(x=0,9,if(((n+(x*10^(i-1)))^7)%(10^i)==m,n=n+(x*10^(i-1));print1(x", ");break)))

%o (PARI) Vecrev(digits(truncate(-(-1/9+O(10^100))^(1/7)))) \\ _Seiichi Manyama_, Aug 04 2019

%o (PARI) N=100; Vecrev(digits(lift(chinese(Mod((1/9+O(2^N))^(1/7), 2^N), Mod((1/9+O(5^N))^(1/7), 5^N)))), N) \\ _Seiichi Manyama_, Aug 04 2019

%Y Digits of 10-adic integers:

%Y A225443 ((-1/9)^(1/7));

%Y A225446 ( 9^(1/7));

%Y A225449 ( (-9)^(1/7)).

%K nonn,base

%O 0,1

%A _Aswini Vaidyanathan_, May 11 2013

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