cp's OEIS Frontend

A309604 Digits of the 10-adic integer (43/9)^(1/3).

%I A309604 #18 Aug 12 2019 02:40:18
%S A309604 3,0,6,8,5,0,7,1,6,9,9,9,1,7,3,8,5,6,2,9,8,1,0,9,6,8,3,0,5,1,5,1,5,7,
%T A309604 7,1,1,5,9,9,9,9,1,2,9,9,2,1,0,3,6,9,9,5,9,4,0,5,3,0,3,0,7,9,8,1,4,6,
%U A309604 7,9,8,7,9,4,2,0,6,6,0,5,4,3,7,9,6,8,6,4,8,5,9,4,1,7,4,2,7,3,5,0
%N A309604 Digits of the 10-adic integer (43/9)^(1/3).
%H A309604 Seiichi Manyama, <a href="/A309604/b309604.txt">Table of n, a(n) for n = 0..10000</a>
%F A309604 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 - 43) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309604       3^3 == 7      (mod 10).
%e A309604       3^3 == 27     (mod 10^2).
%e A309604     603^3 == 227    (mod 10^3).
%e A309604    8603^3 == 2227   (mod 10^4).
%e A309604   58603^3 == 22227  (mod 10^5).
%e A309604   58603^3 == 222227 (mod 10^6).
%o A309604 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((43/9+O(2^N))^(1/3), 2^N), Mod((43/9+O(5^N))^(1/3), 5^N)))), N)
%o A309604 (Ruby)
%o A309604 def A309604(n)
%o A309604   ary = [3]
%o A309604   a = 3
%o A309604   n.times{|i|
%o A309604     b = (a + 3 * (9 * a ** 3 - 43)) % (10 ** (i + 2))
%o A309604     ary << (b - a) / (10 ** (i + 1))
%o A309604     a = b
%o A309604   }
%o A309604   ary
%o A309604 end
%o A309604 p A309604(100)
%Y A309604 Cf. A309600, A309644.
%K A309604 nonn
%O A309604 0,1
%A A309604 _Seiichi Manyama_, Aug 09 2019