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A309612 Digits of the 10-adic integer (-23/9)^(1/3).

%I A309612 #22 Aug 12 2019 10:17:09
%S A309612 7,3,7,0,2,3,9,5,2,5,7,6,5,0,9,7,8,3,4,4,5,4,0,2,6,6,7,3,5,0,3,9,9,3,
%T A309612 5,0,4,6,7,6,8,0,3,6,6,9,4,3,8,8,5,2,7,6,8,3,7,4,2,0,0,2,6,4,8,9,1,5,
%U A309612 7,9,7,3,6,8,3,1,7,3,5,1,5,6,5,4,0,4,6,1,0,1,3,4,2,0,8,2,7,2,3,8
%N A309612 Digits of the 10-adic integer (-23/9)^(1/3).
%H A309612 Seiichi Manyama, <a href="/A309612/b309612.txt">Table of n, a(n) for n = 0..10000</a>
%F A309612 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 23) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n
%e A309612        7^3 == 3      (mod 10).
%e A309612       37^3 == 53     (mod 10^2).
%e A309612      737^3 == 553    (mod 10^3).
%e A309612      737^3 == 5553   (mod 10^4).
%e A309612    20737^3 == 55553  (mod 10^5).
%e A309612   320737^3 == 555553 (mod 10^6).
%o A309612 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-23/9+O(2^N))^(1/3), 2^N), Mod((-23/9+O(5^N))^(1/3), 5^N)))), N)
%o A309612 (Ruby)
%o A309612 def A309612(n)
%o A309612   ary = [7]
%o A309612   a = 7
%o A309612   n.times{|i|
%o A309612     b = (a + 3 * (9 * a ** 3 + 23)) % (10 ** (i + 2))
%o A309612     ary << (b - a) / (10 ** (i + 1))
%o A309612     a = b
%o A309612   }
%o A309612   ary
%o A309612 end
%o A309612 p A309612(100)
%Y A309612 Cf. A173802, A309600, A309609.
%K A309612 nonn,base
%O A309612 0,1
%A A309612 _Seiichi Manyama_, Aug 10 2019