A309824 - OEIS

%I #17 Aug 24 2019 14:21:33

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

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

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

%N Digits of the 10-adic integer (2345678987654321/(1-10^16))^(1/3).

%C x   = ...068250451956420480608557871517841.

%C x^3 = ...123456789876543212345678987654321.

%H Seiichi Manyama, <a href="/A309824/b309824.txt">Table of n, a(n) for n = 0..10000</a>

%e                   1^3 == 1                 (mod 10).

%e                  41^3 == 21                (mod 10^2).

%e                 841^3 == 321               (mod 10^3).

%e                7841^3 == 4321              (mod 10^4).

%e               17841^3 == 54321             (mod 10^5).

%e              517841^3 == 654321            (mod 10^6).

%e             1517841^3 == 7654321           (mod 10^7).

%e            71517841^3 == 87654321          (mod 10^8).

%e           871517841^3 == 987654321         (mod 10^9).

%e          7871517841^3 == 8987654321        (mod 10^10).

%e         57871517841^3 == 78987654321       (mod 10^11).

%e        557871517841^3 == 678987654321      (mod 10^12).

%e       8557871517841^3 == 5678987654321     (mod 10^13).

%e       8557871517841^3 == 45678987654321    (mod 10^14).

%e     608557871517841^3 == 345678987654321   (mod 10^15).

%e     608557871517841^3 == 2345678987654321  (mod 10^16).

%e   80608557871517841^3 == 12345678987654321 (mod 10^17).

%o (PARI) N=100; M=2345678987654321/(1-10^16); 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 (2345678987654321/(1-10^16))^(1/k): this sequence (k=3), A309825 (k=7), A309826 (k=9).

%Y Cf. A309818.

%K nonn,base

%O 0,2

%A _Seiichi Manyama_, Aug 18 2019