A309821 - OEIS

%I #15 Aug 24 2019 10:44:19

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

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

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

%N Digits of the 10-adic integer (123456789/(1-10^9))^(1/3).

%C x   = ...149972824111549982669481257464658829.

%C x^3 = ...123456789123456789123456789123456789.

%H Seiichi Manyama, <a href="/A309821/b309821.txt">Table of n, a(n) for n = 0..10000</a>

%e           9^3 == 9         (mod 10).

%e          29^3 == 89        (mod 10^2).

%e         829^3 == 789       (mod 10^3).

%e        8829^3 == 6789      (mod 10^4).

%e       58829^3 == 56789     (mod 10^5).

%e      658829^3 == 456789    (mod 10^6).

%e     4658829^3 == 3456789   (mod 10^7).

%e    64658829^3 == 23456789  (mod 10^8).

%e   464658829^3 == 123456789 (mod 10^9).

%o (PARI) N=100; M=123456789/(1-10^9); Vecrev(digits(lift(chinese(Mod((M+O(2^N))^(1/3), 2^N), Mod((M+O(5^N))^(1/3), 5^N)))), N)

%Y Digits of the 10-adic integer (123456789/(1-10^9))^(1/k): this sequence (k=3), A309822 (k=7), A309823 (k=9).

%Y Cf. A309818.

%K nonn,base

%O 0,1

%A _Seiichi Manyama_, Aug 18 2019