A309570 - OEIS

%I #32 Aug 12 2019 02:21:23

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

%H Seiichi Manyama, <a href="/A309570/b309570.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) = 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        9^3 == 9      (mod 10).

%e       79^3 == 39     (mod 10^2).

%e      179^3 == 339    (mod 10^3).

%e     6179^3 == 3339   (mod 10^4).

%e    26179^3 == 33339  (mod 10^5).

%e   826179^3 == 333339 (mod 10^6).

%o (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 (Ruby)

%o def A309570(n)

%o   ary = [9]

%o   a = 9

%o   n.times{|i|

%o     b = (a + 3 * a ** 3 - 17) % (10 ** (i + 2))

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

%o     a = b

%o   }

%o   ary

%o end

%o p A309570(100)

%Y Cf. A173764, A309600, A309640.

%K nonn,base

%O 0,1

%A _Seiichi Manyama_, Aug 10 2019