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A309648 Digits of the 10-adic integer (-17/9)^(1/3).

%I A309648 #13 Aug 11 2019 16:18:04
%S A309648 3,8,3,1,2,9,6,6,6,3,4,7,2,1,2,7,3,2,8,8,9,6,6,7,5,4,3,4,6,3,4,6,6,6,
%T A309648 2,4,7,5,2,4,9,7,0,9,3,2,9,1,1,3,3,2,9,8,7,5,4,6,7,1,3,0,2,6,8,3,3,0,
%U A309648 4,9,8,3,5,3,1,9,6,1,4,0,3,8,6,4,6,2,0,2,7,6,3,3,0,9,9,9,4,6,2,2
%N A309648 Digits of the 10-adic integer (-17/9)^(1/3).
%H A309648 Seiichi Manyama, <a href="/A309648/b309648.txt">Table of n, a(n) for n = 0..10000</a>
%F A309648 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 17) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309648        3^3 == 7      (mod 10).
%e A309648       83^3 == 87     (mod 10^2).
%e A309648      383^3 == 887    (mod 10^3).
%e A309648     1383^3 == 8887   (mod 10^4).
%e A309648    21383^3 == 88887  (mod 10^5).
%e A309648   921383^3 == 888887 (mod 10^6).
%o A309648 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-17/9+O(2^N))^(1/3), 2^N), Mod((-17/9+O(5^N))^(1/3), 5^N)))), N)
%o A309648 (Ruby)
%o A309648 def A309648(n)
%o A309648   ary = [3]
%o A309648   a = 3
%o A309648   n.times{|i|
%o A309648     b = (a + 3 * (9 * a ** 3 + 17)) % (10 ** (i + 2))
%o A309648     ary << (b - a) / (10 ** (i + 1))
%o A309648     a = b
%o A309648   }
%o A309648   ary
%o A309648 end
%o A309648 p A309648(100)
%Y A309648 Cf. A309600
%K A309648 nonn,base
%O A309648 0,1
%A A309648 _Seiichi Manyama_, Aug 11 2019