cp's OEIS Frontend

A309606 Digits of the 10-adic integer (-7/3)^(1/3).

%I A309606 #23 Aug 12 2019 02:39:49
%S A309606 1,1,0,4,6,7,6,7,5,8,3,7,0,5,9,7,8,0,8,8,1,6,9,1,7,4,9,2,4,9,4,7,4,6,
%T A309606 3,2,5,4,7,0,0,9,9,2,7,7,5,4,0,2,9,8,2,3,0,5,9,8,2,9,2,9,3,0,1,8,4,0,
%U A309606 2,9,1,7,1,3,1,9,5,8,1,2,4,0,3,5,2,7,2,3,5,5,5,6,5,9,9,4,1,1,0,9
%N A309606 Digits of the 10-adic integer (-7/3)^(1/3).
%H A309606 Seiichi Manyama, <a href="/A309606/b309606.txt">Table of n, a(n) for n = 0..10000</a>
%F A309606 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 1, b(n) = b(n-1) + 3 * b(n-1)^3 + 7 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309606        1^3 == 1      (mod 10).
%e A309606       11^3 == 31     (mod 10^2).
%e A309606       11^3 == 331    (mod 10^3).
%e A309606     4011^3 == 3331   (mod 10^4).
%e A309606    64011^3 == 33331  (mod 10^5).
%e A309606   764011^3 == 333331 (mod 10^6).
%p A309606 op([1,3],padic:-rootp(x^3+7/3,10,100)); # _Robert Israel_, Aug 09 2019
%o A309606 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-7/3+O(2^N))^(1/3), 2^N), Mod((-7/3+O(5^N))^(1/3), 5^N)))), N)
%o A309606 (Ruby)
%o A309606 def A309606(n)
%o A309606   ary = [1]
%o A309606   a = 1
%o A309606   n.times{|i|
%o A309606     b = (a + 3 * a ** 3 + 7) % (10 ** (i + 2))
%o A309606     ary << (b - a) / (10 ** (i + 1))
%o A309606     a = b
%o A309606   }
%o A309606   ary
%o A309606 end
%o A309606 p A309606(100)
%Y A309606 Cf. A309600, A309642.
%K A309606 nonn
%O A309606 0,4
%A A309606 _Seiichi Manyama_, Aug 09 2019