A309608 - OEIS

%I #23 Aug 12 2019 10:17:25

%S 7,0,3,0,3,3,7,4,3,3,4,2,5,1,7,3,8,4,7,6,4,5,0,4,8,7,8,4,6,3,0,2,8,3,

%T 2,4,4,6,2,3,5,0,4,6,8,2,0,1,9,5,5,4,2,8,7,8,6,6,5,0,8,9,8,2,3,8,0,1,

%U 9,5,8,6,2,3,2,8,7,7,9,8,8,4,5,0,7,4,7,1,0,2,4,9,0,8,5,4,5,0,2,6

%N Digits of the 10-adic integer (-13/9)^(1/3).

%H Seiichi Manyama, <a href="/A309608/b309608.txt">Table of n, a(n) for n = 0..10000</a>

%F 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 + 13) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

%e        7^3 == 3      (mod 10).

%e        7^3 == 43     (mod 10^2).

%e      307^3 == 443    (mod 10^3).

%e      307^3 == 4443   (mod 10^4).

%e    30307^3 == 44443  (mod 10^5).

%e   330307^3 == 444443 (mod 10^6).

%o (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-13/9+O(2^N))^(1/3), 2^N), Mod((-13/9+O(5^N))^(1/3), 5^N)))), N)

%o (Ruby)

%o def A309608(n)

%o   ary = [7]

%o   a = 7

%o   n.times{|i|

%o     b = (a + 3 * (9 * a ** 3 + 13)) % (10 ** (i + 2))

%o     ary << (b - a) / (10 ** (i + 1))

%o     a = b

%o   }

%o   ary

%o end

%o p A309608(100)

%Y Cf. A173770, A309600, A309613.

%K nonn,base

%O 0,1

%A _Seiichi Manyama_, Aug 10 2019