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A309610 Digits of the 10-adic integer (41/9)^(1/3).

%I A309610 #22 Aug 12 2019 10:17:17
%S A309610 9,4,6,5,9,6,4,6,9,6,3,6,9,7,3,3,0,2,6,9,3,9,8,4,7,8,8,6,1,5,5,7,1,8,
%T A309610 4,4,0,3,6,1,8,2,1,5,9,2,0,3,8,9,5,6,4,1,5,7,2,0,1,8,9,8,3,1,1,7,3,6,
%U A309610 8,6,1,3,7,2,5,7,1,7,7,3,7,1,7,6,9,7,1,7,0,3,1,8,7,3,1,0,6,2,3,3
%N A309610 Digits of the 10-adic integer (41/9)^(1/3).
%H A309610 Seiichi Manyama, <a href="/A309610/b309610.txt">Table of n, a(n) for n = 0..10000</a>
%F A309610 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 - 41) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n
%e A309610        9^3 == 9      (mod 10).
%e A309610       49^3 == 49     (mod 10^2).
%e A309610      649^3 == 449    (mod 10^3).
%e A309610     5649^3 == 4449   (mod 10^4).
%e A309610    95649^3 == 44449  (mod 10^5).
%e A309610   695649^3 == 444449 (mod 10^6).
%o A309610 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((41/9+O(2^N))^(1/3), 2^N), Mod((41/9+O(5^N))^(1/3), 5^N)))), N)
%o A309610 (Ruby)
%o A309610 def A309610(n)
%o A309610   ary = [9]
%o A309610   a = 9
%o A309610   n.times{|i|
%o A309610     b = (a + 7 * (9 * a ** 3 - 41)) % (10 ** (i + 2))
%o A309610     ary << (b - a) / (10 ** (i + 1))
%o A309610     a = b
%o A309610   }
%o A309610   ary
%o A309610 end
%o A309610 p A309610(100)
%Y A309610 Cf. A173776, A309600, A309611.
%K A309610 nonn,base
%O A309610 0,1
%A A309610 _Seiichi Manyama_, Aug 10 2019