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A309640 Digits of the 10-adic integer (-17/3)^(1/3).

%I A309640 #13 Aug 12 2019 10:16:57
%S A309640 1,2,8,3,7,1,3,3,7,8,5,8,6,3,1,0,4,5,4,9,8,0,0,8,7,1,1,0,6,8,8,2,3,0,
%T A309640 0,7,4,7,4,7,0,4,3,0,7,9,9,8,2,6,5,4,6,8,7,6,7,2,6,8,4,4,5,4,7,5,3,3,
%U A309640 1,7,4,3,3,3,1,9,9,0,9,0,1,1,2,9,3,8,3,8,4,1,8,7,5,7,4,9,6,7,2,7
%N A309640 Digits of the 10-adic integer (-17/3)^(1/3).
%H A309640 Seiichi Manyama, <a href="/A309640/b309640.txt">Table of n, a(n) for n = 0..10000</a>
%F A309640 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 1, b(n) = b(n-1) + 3 * b(n-1)^3 + 17 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309640        1^3 == 1      (mod 10).
%e A309640       21^3 == 61     (mod 10^2).
%e A309640      821^3 == 661    (mod 10^3).
%e A309640     3821^3 == 6661   (mod 10^4).
%e A309640    73821^3 == 66661  (mod 10^5).
%e A309640   173821^3 == 666661 (mod 10^6).
%o A309640 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-17/3+O(2^N))^(1/3), 2^N), Mod((-17/3+O(5^N))^(1/3), 5^N)))), N)
%o A309640 (Ruby)
%o A309640 def A309640(n)
%o A309640   ary = [1]
%o A309640   a = 1
%o A309640   n.times{|i|
%o A309640     b = (a + 3 * a ** 3 + 17) % (10 ** (i + 2))
%o A309640     ary << (b - a) / (10 ** (i + 1))
%o A309640     a = b
%o A309640   }
%o A309640   ary
%o A309640 end
%o A309640 p A309640(100)
%Y A309640 Cf. A309570, A309600.
%K A309640 nonn,base
%O A309640 0,2
%A A309640 _Seiichi Manyama_, Aug 11 2019