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A309614 Digits of the 10-adic integer (31/9)^(1/3).

%I A309614 #18 Aug 12 2019 10:17:01
%S A309614 9,1,9,8,8,1,3,3,5,8,3,9,6,0,0,9,0,6,1,9,2,8,3,4,4,7,9,1,1,5,3,2,0,1,
%T A309614 6,9,3,2,9,2,5,9,4,0,0,4,7,9,3,2,1,0,2,1,2,7,8,7,9,2,5,1,1,5,6,3,9,3,
%U A309614 1,7,8,5,7,1,3,2,9,4,2,5,0,2,2,4,1,5,4,0,4,2,1,5,2,0,5,5,6,2,0,8
%N A309614 Digits of the 10-adic integer (31/9)^(1/3).
%H A309614 Seiichi Manyama, <a href="/A309614/b309614.txt">Table of n, a(n) for n = 0..10000</a>
%F A309614 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 - 31) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309614        9^3 == 9      (mod 10).
%e A309614       19^3 == 59     (mod 10^2).
%e A309614      919^3 == 559    (mod 10^3).
%e A309614     8919^3 == 5559   (mod 10^4).
%e A309614    88919^3 == 55559  (mod 10^5).
%e A309614   188919^3 == 555559 (mod 10^6).
%o A309614 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((31/9+O(2^N))^(1/3), 2^N), Mod((31/9+O(5^N))^(1/3), 5^N)))), N)
%o A309614 (Ruby)
%o A309614 def A309614(n)
%o A309614   ary = [9]
%o A309614   a = 9
%o A309614   n.times{|i|
%o A309614     b = (a + 7 * (9 * a ** 3 - 31)) % (10 ** (i + 2))
%o A309614     ary << (b - a) / (10 ** (i + 1))
%o A309614     a = b
%o A309614   }
%o A309614   ary
%o A309614 end
%o A309614 p A309614(100)
%Y A309614 Cf. A309595, A309600.
%K A309614 nonn,base
%O A309614 0,1
%A A309614 _Seiichi Manyama_, Aug 10 2019