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A309647 Digits of the 10-adic integer (-53/9)^(1/3).

%I A309647 #14 Aug 11 2019 11:59:56
%S A309647 7,2,6,1,3,2,9,4,6,9,1,4,6,5,1,8,6,9,0,9,6,7,0,7,6,3,6,7,5,6,4,8,4,7,
%T A309647 0,1,9,2,3,9,6,0,0,5,7,4,6,9,6,7,9,6,7,1,7,1,2,1,6,8,9,9,5,3,5,8,1,0,
%U A309647 5,1,4,6,4,6,2,6,8,3,2,0,8,8,1,4,9,7,4,2,3,6,1,0,5,7,2,6,9,6,3,3
%N A309647 Digits of the 10-adic integer (-53/9)^(1/3).
%H A309647 Seiichi Manyama, <a href="/A309647/b309647.txt">Table of n, a(n) for n = 0..10000</a>
%F A309647 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 53) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309647        7^3 == 3      (mod 10).
%e A309647       27^3 == 83     (mod 10^2).
%e A309647      627^3 == 883    (mod 10^3).
%e A309647     1627^3 == 8883   (mod 10^4).
%e A309647    31627^3 == 88883  (mod 10^5).
%e A309647   231627^3 == 888883 (mod 10^6).
%o A309647 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-53/9+O(2^N))^(1/3), 2^N), Mod((-53/9+O(5^N))^(1/3), 5^N)))), N)
%o A309647 (Ruby)
%o A309647 def A309647(n)
%o A309647   ary = [7]
%o A309647   a = 7
%o A309647   n.times{|i|
%o A309647     b = (a + 3 * (9 * a ** 3 + 53)) % (10 ** (i + 2))
%o A309647     ary << (b - a) / (10 ** (i + 1))
%o A309647     a = b
%o A309647   }
%o A309647   ary
%o A309647 end
%o A309647 p A309647(100)
%Y A309647 Cf. A309600, A309601.
%K A309647 nonn,base
%O A309647 0,1
%A A309647 _Seiichi Manyama_, Aug 11 2019