cp's OEIS Frontend

A309644 Digits of the 10-adic integer (-43/9)^(1/3).

%I A309644 #14 Aug 12 2019 02:38:52
%S A309644 7,9,3,1,4,9,2,8,3,0,0,0,8,2,6,1,4,3,7,0,1,8,9,0,3,1,6,9,4,8,4,8,4,2,
%T A309644 2,8,8,4,0,0,0,0,8,7,0,0,7,8,9,6,3,0,0,4,0,5,9,4,6,9,6,9,2,0,1,8,5,3,
%U A309644 2,0,1,2,0,5,7,9,3,3,9,4,5,6,2,0,3,1,3,5,1,4,0,5,8,2,5,7,2,6,4,9
%N A309644 Digits of the 10-adic integer (-43/9)^(1/3).
%H A309644 Seiichi Manyama, <a href="/A309644/b309644.txt">Table of n, a(n) for n = 0..10000</a>
%F A309644 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 + 43) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309644        7^3 == 3      (mod 10).
%e A309644       97^3 == 73     (mod 10^2).
%e A309644      397^3 == 773    (mod 10^3).
%e A309644     1397^3 == 7773   (mod 10^4).
%e A309644    41397^3 == 77773  (mod 10^5).
%e A309644   941397^3 == 777773 (mod 10^6).
%o A309644 (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 A309644 (Ruby)
%o A309644 def A309644(n)
%o A309644   ary = [7]
%o A309644   a = 7
%o A309644   n.times{|i|
%o A309644     b = (a + 3 * (9 * a ** 3 + 43)) % (10 ** (i + 2))
%o A309644     ary << (b - a) / (10 ** (i + 1))
%o A309644     a = b
%o A309644   }
%o A309644   ary
%o A309644 end
%o A309644 p A309644(100)
%Y A309644 Cf. A309600, A309604.
%K A309644 nonn,base
%O A309644 0,1
%A A309644 _Seiichi Manyama_, Aug 11 2019