A225451 - OEIS

%I #12 Aug 16 2019 12:16:41

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

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

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

%N 10-adic integer x such that x^7 = 1/3.

%C This is the 10's complement of A225442.

%H Seiichi Manyama, <a href="/A225451/b225451.txt">Table of n, a(n) for n = 0..10000</a>

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

%e       63^7 == -33     (mod 10^2).

%e      563^7 == -333    (mod 10^3).

%e     2563^7 == -3333   (mod 10^4).

%e    42563^7 == -33333  (mod 10^5).

%e   742563^7 == -333333 (mod 10^6).

%o (PARI) n=0;for(i=1,100,m=(2*(10^i-1)/3)+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) N=100; Vecrev(digits(lift(chinese(Mod((1/3+O(2^N))^(1/7), 2^N), Mod((1/3+O(5^N))^(1/7), 5^N)))), N) \\ _Seiichi Manyama_, Aug 06 2019

%Y Cf. A225442.

%K nonn,base

%O 0,1

%A _Aswini Vaidyanathan_, May 11 2013