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A309643 Digits of the 10-adic integer (-61/9)^(1/3).

%I A309643 #15 Aug 12 2019 02:39:03
%S A309643 1,9,4,9,4,5,2,8,0,8,3,9,0,1,4,2,8,9,2,6,8,9,0,4,8,5,0,0,4,2,0,6,9,8,
%T A309643 8,0,9,8,5,8,5,9,3,5,5,8,1,9,9,8,2,3,0,8,4,6,1,8,5,7,3,2,8,6,6,0,1,9,
%U A309643 5,4,6,2,7,4,7,2,4,4,5,3,8,9,9,7,7,6,7,9,2,6,5,7,2,2,8,9,6,8,9,0
%N A309643 Digits of the 10-adic integer (-61/9)^(1/3).
%H A309643 Seiichi Manyama, <a href="/A309643/b309643.txt">Table of n, a(n) for n = 0..10000</a>
%F A309643 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 + 61) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309643        1^3 == 1      (mod 10).
%e A309643       91^3 == 71     (mod 10^2).
%e A309643      491^3 == 771    (mod 10^3).
%e A309643     9491^3 == 7771   (mod 10^4).
%e A309643    49491^3 == 77771  (mod 10^5).
%e A309643   549491^3 == 777771 (mod 10^6).
%o A309643 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-61/9+O(2^N))^(1/3), 2^N), Mod((-61/9+O(5^N))^(1/3), 5^N)))), N)
%o A309643 (Ruby)
%o A309643 def A309643(n)
%o A309643   ary = [1]
%o A309643   a = 1
%o A309643   n.times{|i|
%o A309643     b = (a + 7 * (9 * a ** 3 + 61)) % (10 ** (i + 2))
%o A309643     ary << (b - a) / (10 ** (i + 1))
%o A309643     a = b
%o A309643   }
%o A309643   ary
%o A309643 end
%o A309643 p A309643(100)
%Y A309643 Cf. A309600, A309605.
%K A309643 nonn,base
%O A309643 0,2
%A A309643 _Seiichi Manyama_, Aug 11 2019