cp's OEIS Frontend

A309645 Digits of the 10-adic integer (11/9)^(1/3).

%I A309645 #23 Aug 12 2019 10:16:39
%S A309645 9,5,8,6,6,5,0,7,6,0,5,1,0,8,9,4,8,5,8,5,6,2,2,5,2,1,8,7,6,9,9,8,2,3,
%T A309645 8,1,0,5,8,5,7,0,0,9,6,7,4,2,0,6,6,7,7,1,2,4,1,7,9,1,2,5,4,8,7,7,3,4,
%U A309645 4,9,1,7,6,9,6,7,0,7,4,1,3,3,6,9,7,4,6,9,8,8,5,9,0,0,1,5,4,0,5,4
%N A309645 Digits of the 10-adic integer (11/9)^(1/3).
%H A309645 Seiichi Manyama, <a href="/A309645/b309645.txt">Table of n, a(n) for n = 0..10000</a>
%F A309645 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 - 11) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309645        9^3 == 9      (mod 10).
%e A309645       59^3 == 79     (mod 10^2).
%e A309645      859^3 == 779    (mod 10^3).
%e A309645     6859^3 == 7779   (mod 10^4).
%e A309645    66859^3 == 77779  (mod 10^5).
%e A309645   566859^3 == 777779 (mod 10^6).
%o A309645 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((11/9+O(2^N))^(1/3), 2^N), Mod((11/9+O(5^N))^(1/3), 5^N)))), N)
%o A309645 (Ruby)
%o A309645 def A309645(n)
%o A309645   ary = [9]
%o A309645   a = 9
%o A309645   n.times{|i|
%o A309645     b = (a + 7 * (9 * a ** 3 - 11)) % (10 ** (i + 2))
%o A309645     ary << (b - a) / (10 ** (i + 1))
%o A309645     a = b
%o A309645   }
%o A309645   ary
%o A309645 end
%o A309645 p A309645(100)
%Y A309645 Cf. A309600, A309603.
%K A309645 nonn,base
%O A309645 0,1
%A A309645 _Seiichi Manyama_, Aug 11 2019