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A309646 Digits of the 10-adic integer (-71/9)^(1/3).

%I A309646 #14 Aug 11 2019 12:00:16
%S A309646 1,6,3,1,6,7,2,5,4,5,8,8,0,7,7,0,9,9,6,5,4,1,8,9,2,8,3,5,3,4,6,9,6,8,
%T A309646 4,3,0,2,6,7,5,7,5,7,9,3,7,7,9,7,6,3,2,1,5,3,4,8,4,2,4,9,0,5,5,9,0,4,
%U A309646 4,8,0,9,7,5,2,2,3,3,5,9,8,9,3,7,0,3,1,6,0,2,0,3,9,7,6,5,3,1,3,1
%N A309646 Digits of the 10-adic integer (-71/9)^(1/3).
%H A309646 Seiichi Manyama, <a href="/A309646/b309646.txt">Table of n, a(n) for n = 0..10000</a>
%F A309646 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 1, 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 A309646        1^3 == 1      (mod 10).
%e A309646       61^3 == 81     (mod 10^2).
%e A309646      361^3 == 881    (mod 10^3).
%e A309646     1361^3 == 8881   (mod 10^4).
%e A309646    61361^3 == 88881  (mod 10^5).
%e A309646   761361^3 == 888881 (mod 10^6).
%o A309646 (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 A309646 (Ruby)
%o A309646 def A309646(n)
%o A309646   ary = [1]
%o A309646   a = 1
%o A309646   n.times{|i|
%o A309646     b = (a + 7 * (9 * a ** 3 + 71)) % (10 ** (i + 2))
%o A309646     ary << (b - a) / (10 ** (i + 1))
%o A309646     a = b
%o A309646   }
%o A309646   ary
%o A309646 end
%o A309646 p A309646(100)
%Y A309646 Cf. A309600, A309602.
%K A309646 nonn,base
%O A309646 0,2
%A A309646 _Seiichi Manyama_, Aug 11 2019