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A306555 Expansion of the 10-adic cube root of -1/13, that is, the 10-adic integer solution to x^3 = -1/13.

%I A306555 #13 Mar 25 2019 04:21:50
%S A306555 7,4,3,5,8,0,6,7,1,2,5,9,1,6,3,4,2,2,9,0,1,7,2,4,8,5,1,9,0,4,8,3,9,3,
%T A306555 7,8,6,7,7,3,5,7,2,9,3,1,3,8,6,6,7,7,9,9,8,4,3,2,0,3,7,2,1,5,7,3,6,3,
%U A306555 6,9,8,9,5,4,4,3,3,8,6,4,5,6,6,6,8,2,9
%N A306555 Expansion of the 10-adic cube root of -1/13, that is, the 10-adic integer solution to x^3 = -1/13.
%C A306555 10's complement of A306554.
%H A306555 Robert Israel, <a href="/A306555/b306555.txt">Table of n, a(n) for n = 1..10000</a>
%F A306555 a(n) = 9 - A306554(n) for n >= 2.
%e A306555 7^3 == 3 == -1/13 (mod 10).
%e A306555 47^3 == 23 == -1/13 (mod 100).
%e A306555 347^3 == 923 == -1/13 (mod 1000).
%e A306555 5347^3 == 6923 == -1/13 (mod 10000).
%e A306555 ...
%e A306555 ...952176085347^3 = ...076923076923 = ...999999999999/13 = -1/13.
%p A306555 op([1,3],padic:-rootp(13*x^3+1,10,100)); # _Robert Israel_, Mar 24 2019
%o A306555 (PARI) seq(n)={Vecrev(digits(lift(chinese( Mod((-1/13 + O(5^n))^(1/3), 5^n), Mod((-1/13 + O(2^n))^(1/3), 2^n)))), n)} \\ Following _Andrew Howroyd_'s code for A319740.
%Y A306555 10-adic cube root of p/q:
%Y A306555 q=1: A225409 (p=-9), A225408 (p=-7), A225407 (p=-3), A225404 (p=3), A225405 (p=7), A225406 (p=9);
%Y A306555 q=3: A225402 (p=-1), A225411 (p=1);
%Y A306555 q=7: A306552 (p=-1), A319739 (p=1);
%Y A306555 q=9: A225401 (p=-7), A153042 (p=-1), A225412 (p=1), A225410 (p=7);
%Y A306555 q=11: A306553 (p=-1), A319740 (p=1);
%Y A306555 q=13: this sequence (p=-1), A306554 (p=1).
%K A306555 nonn,base
%O A306555 1,1
%A A306555 _Jianing Song_, Feb 23 2019