cp's OEIS Frontend

A309570 Digits of the 10-adic integer (17/3)^(1/3).

%I A309570 #32 Aug 12 2019 02:21:23
%S A309570 9,7,1,6,2,8,6,6,2,1,4,1,3,6,8,9,5,4,5,0,1,9,9,1,2,8,8,9,3,1,1,7,6,9,
%T A309570 9,2,5,2,5,2,9,5,6,9,2,0,0,1,7,3,4,5,3,1,2,3,2,7,3,1,5,5,4,5,2,4,6,6,
%U A309570 8,2,5,6,6,6,8,0,0,9,0,9,8,8,7,0,6,1,6,1,5,8,1,2,4,2,5,0,3,2,7,2
%N A309570 Digits of the 10-adic integer (17/3)^(1/3).
%H A309570 Seiichi Manyama, <a href="/A309570/b309570.txt">Table of n, a(n) for n = 0..10000</a>
%F A309570 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 3 * b(n-1)^3 - 17 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309570        9^3 == 9      (mod 10).
%e A309570       79^3 == 39     (mod 10^2).
%e A309570      179^3 == 339    (mod 10^3).
%e A309570     6179^3 == 3339   (mod 10^4).
%e A309570    26179^3 == 33339  (mod 10^5).
%e A309570   826179^3 == 333339 (mod 10^6).
%o A309570 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((17/3+O(2^N))^(1/3), 2^N), Mod((17/3+O(5^N))^(1/3), 5^N)))), N)
%o A309570 (Ruby)
%o A309570 def A309570(n)
%o A309570   ary = [9]
%o A309570   a = 9
%o A309570   n.times{|i|
%o A309570     b = (a + 3 * a ** 3 - 17) % (10 ** (i + 2))
%o A309570     ary << (b - a) / (10 ** (i + 1))
%o A309570     a = b
%o A309570   }
%o A309570   ary
%o A309570 end
%o A309570 p A309570(100)
%Y A309570 Cf. A173764, A309600, A309640.
%K A309570 nonn,base
%O A309570 0,1
%A A309570 _Seiichi Manyama_, Aug 10 2019