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A309602 Digits of the 10-adic integer (71/9)^(1/3).

%I A309602 #20 Aug 12 2019 02:40:52
%S A309602 9,3,6,8,3,2,7,4,5,4,1,1,9,2,2,9,0,0,3,4,5,8,1,0,7,1,6,4,6,5,3,0,3,1,
%T A309602 5,6,9,7,3,2,4,2,4,2,0,6,2,2,0,2,3,6,7,8,4,6,5,1,5,7,5,0,9,4,4,0,9,5,
%U A309602 5,1,9,0,2,4,7,7,6,6,4,0,1,0,6,2,9,6,8,3,9,7,9,6,0,2,3,4,6,8,6,8
%N A309602 Digits of the 10-adic integer (71/9)^(1/3).
%H A309602 Seiichi Manyama, <a href="/A309602/b309602.txt">Table of n, a(n) for n = 0..10000</a>
%F A309602 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 - 71) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309602        9^3 == 9      (mod 10).
%e A309602       39^3 == 19     (mod 10^2).
%e A309602      639^3 == 119    (mod 10^3).
%e A309602     8639^3 == 1119   (mod 10^4).
%e A309602    38639^3 == 11119  (mod 10^5).
%e A309602   238639^3 == 111119 (mod 10^6).
%o A309602 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((71/9+O(2^N))^(1/3), 2^N), Mod((71/9+O(5^N))^(1/3), 5^N)))), N)
%o A309602 (Ruby)
%o A309602 def A309602(n)
%o A309602   ary = [9]
%o A309602   a = 9
%o A309602   n.times{|i|
%o A309602     b = (a + 7 * (9 * a ** 3 - 71)) % (10 ** (i + 2))
%o A309602     ary << (b - a) / (10 ** (i + 1))
%o A309602     a = b
%o A309602   }
%o A309602   ary
%o A309602 end
%o A309602 p A309602(100)
%Y A309602 Cf. A165247, A309600, A309646.
%K A309602 nonn
%O A309602 0,1
%A A309602 _Seiichi Manyama_, Aug 09 2019