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A309642 Digits of the 10-adic integer (7/3)^(1/3).

%I A309642 #15 Aug 12 2019 02:39:37
%S A309642 9,8,9,5,3,2,3,2,4,1,6,2,9,4,0,2,1,9,1,1,8,3,0,8,2,5,0,7,5,0,5,2,5,3,
%T A309642 6,7,4,5,2,9,9,0,0,7,2,2,4,5,9,7,0,1,7,6,9,4,0,1,7,0,7,0,6,9,8,1,5,9,
%U A309642 7,0,8,2,8,6,8,0,4,1,8,7,5,9,6,4,7,2,7,6,4,4,4,3,4,0,0,5,8,8,9,0
%N A309642 Digits of the 10-adic integer (7/3)^(1/3).
%H A309642 Seiichi Manyama, <a href="/A309642/b309642.txt">Table of n, a(n) for n = 0..10000</a>
%F A309642 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 3 * b(n-1)^3 - 7 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309642        9^3 == 9      (mod 10).
%e A309642       89^3 == 69     (mod 10^2).
%e A309642      989^3 == 669    (mod 10^3).
%e A309642     5989^3 == 6669   (mod 10^4).
%e A309642    35989^3 == 66669  (mod 10^5).
%e A309642   235989^3 == 666669 (mod 10^6).
%o A309642 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((7/3+O(2^N))^(1/3), 2^N), Mod((7/3+O(5^N))^(1/3), 5^N)))), N)
%o A309642 (Ruby)
%o A309642 def A309642(n)
%o A309642   ary = [9]
%o A309642   a = 9
%o A309642   n.times{|i|
%o A309642     b = (a + 3 * a ** 3 - 7) % (10 ** (i + 2))
%o A309642     ary << (b - a) / (10 ** (i + 1))
%o A309642     a = b
%o A309642   }
%o A309642   ary
%o A309642 end
%o A309642 p A309642(100)
%Y A309642 Cf. A309600, A309606.
%K A309642 nonn
%O A309642 0,1
%A A309642 _Seiichi Manyama_, Aug 11 2019