A309822 - OEIS

%I #12 Aug 24 2019 10:46:51

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

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

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

%N Digits of the 10-adic integer (123456789/(1-10^9))^(1/7).

%C x   = ...360427291675787237496648325197272669.

%C x^7 = ...123456789123456789123456789123456789.

%H Seiichi Manyama, <a href="/A309822/b309822.txt">Table of n, a(n) for n = 0..10000</a>

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

%e          69^7 == 89        (mod 10^2).

%e         669^7 == 789       (mod 10^3).

%e        2669^7 == 6789      (mod 10^4).

%e       72669^7 == 56789     (mod 10^5).

%e      272669^7 == 456789    (mod 10^6).

%e     7272669^7 == 3456789   (mod 10^7).

%e    97272669^7 == 23456789  (mod 10^8).

%e   197272669^7 == 123456789 (mod 10^9).

%o (PARI) N=100; M=123456789/(1-10^9); Vecrev(digits(lift(chinese(Mod((M+O(2^N))^(1/7), 2^N), Mod((M+O(5^N))^(1/7), 5^N)))), N)

%Y Digits of the 10-adic integer (123456789/(1-10^9))^(1/k): A309821 (k=3), this sequence (k=7), A309823 (k=9).

%Y Cf. A309819.

%K nonn,base

%O 0,1

%A _Seiichi Manyama_, Aug 18 2019