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A309609 Digits of the 10-adic integer (23/9)^(1/3).

%I A309609 #21 Aug 12 2019 10:17:20
%S A309609 3,6,2,9,7,6,0,4,7,4,2,3,4,9,0,2,1,6,5,5,4,5,9,7,3,3,2,6,4,9,6,0,0,6,
%T A309609 4,9,5,3,2,3,1,9,6,3,3,0,5,6,1,1,4,7,2,3,1,6,2,5,7,9,9,7,3,5,1,0,8,4,
%U A309609 2,0,2,6,3,1,6,8,2,6,4,8,4,3,4,5,9,5,3,8,9,8,6,5,7,9,1,7,2,7,6,1
%N A309609 Digits of the 10-adic integer (23/9)^(1/3).
%H A309609 Seiichi Manyama, <a href="/A309609/b309609.txt">Table of n, a(n) for n = 0..10000</a>
%F A309609 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, 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 A309609        3^3 == 7      (mod 10).
%e A309609       63^3 == 47     (mod 10^2).
%e A309609      263^3 == 447    (mod 10^3).
%e A309609     9263^3 == 4447   (mod 10^4).
%e A309609    79263^3 == 44447  (mod 10^5).
%e A309609   679263^3 == 444447 (mod 10^6).
%o A309609 (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 A309609 (Ruby)
%o A309609 def A309609(n)
%o A309609   ary = [3]
%o A309609   a = 3
%o A309609   n.times{|i|
%o A309609     b = (a + 3 * (9 * a ** 3 - 23)) % (10 ** (i + 2))
%o A309609     ary << (b - a) / (10 ** (i + 1))
%o A309609     a = b
%o A309609   }
%o A309609   ary
%o A309609 end
%o A309609 p A309609(100)
%Y A309609 Cf. A173772, A309600, A309612.
%K A309609 nonn,base
%O A309609 0,1
%A A309609 _Seiichi Manyama_, Aug 10 2019