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A309641 Digits of the 10-adic integer (-11/3)^(1/3).

%I A309641 #13 Aug 12 2019 02:38:20
%S A309641 7,6,7,7,4,1,3,1,6,8,2,6,7,3,8,9,9,8,6,7,4,6,6,4,4,4,9,1,1,0,9,0,8,2,
%T A309641 6,7,0,5,6,0,0,1,6,6,9,8,5,7,2,3,0,4,8,4,0,6,7,4,6,2,6,8,5,1,0,2,9,8,
%U A309641 0,8,8,5,8,5,2,5,0,9,2,2,8,7,5,0,6,5,6,1,9,1,8,1,0,1,6,4,4,8,0,7
%N A309641 Digits of the 10-adic integer (-11/3)^(1/3).
%H A309641 Seiichi Manyama, <a href="/A309641/b309641.txt">Table of n, a(n) for n = 0..10000</a>
%F A309641 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 9 * (3 * b(n-1)^3 + 11) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309641        7^3 == 3      (mod 10).
%e A309641       67^3 == 63     (mod 10^2).
%e A309641      767^3 == 663    (mod 10^3).
%e A309641     7767^3 == 6663   (mod 10^4).
%e A309641    47767^3 == 66663  (mod 10^5).
%e A309641   147767^3 == 666663 (mod 10^6).
%o A309641 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-11/3+O(2^N))^(1/3), 2^N), Mod((-11/3+O(5^N))^(1/3), 5^N)))), N)
%o A309641 (Ruby)
%o A309641 def A309641(n)
%o A309641   ary = [7]
%o A309641   a = 7
%o A309641   n.times{|i|
%o A309641     b = (a + 9 * (3 * a ** 3 + 11)) % (10 ** (i + 2))
%o A309641     ary << (b - a) / (10 ** (i + 1))
%o A309641     a = b
%o A309641   }
%o A309641   ary
%o A309641 end
%o A309641 p A309641(100)
%Y A309641 Cf. A309569, A309600.
%K A309641 nonn,base
%O A309641 0,1
%A A309641 _Seiichi Manyama_, Aug 11 2019