A225443 - OEIS

%I #31 Aug 14 2019 08:31:40

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

%T 4,0,8,4,1,3,1,9,8,3,1,7,7,8,4,2,0,6,9,6,8,6,6,0,0,1,7,0,9,8,8,6,6,0,

%U 7,2,1,3,3,5,9,7,3,3,7,3,9,4,5,4,5,2,3,7,6,7,3,5,5,3,7,7,3,3,7,3

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

%H Seiichi Manyama, <a href="/A225443/b225443.txt">Table of n, a(n) for n = 0..10000</a>

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

%e       31^7 == 11     (mod 10^2).

%e       31^7 == 111    (mod 10^3).

%e     1031^7 == 1111   (mod 10^4).

%e    91031^7 == 11111  (mod 10^5).

%e   191031^7 == 111111 (mod 10^6).

%o (PARI) n=0;for(i=1,100,m=(10^i-1)/9;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 A225446 (    9^(1/7));

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

%Y A225452 ((1/9)^(1/7)).

%K nonn,base

%O 0,2

%A _Aswini Vaidyanathan_, May 11 2013