%I #41 Aug 11 2019 11:18:41
%S 7,1,6,8,7,0,3,3,3,6,5,2,7,8,7,2,6,7,1,1,0,3,3,2,4,5,6,5,3,6,5,3,3,3,
%T 7,5,2,4,7,5,0,2,9,0,6,7,0,8,8,6,6,7,0,1,2,4,5,3,2,8,6,9,7,3,1,6,6,9,
%U 5,0,1,6,4,6,8,0,3,8,5,9,6,1,3,5,3,7,9,7,2,3,6,6,9,0,0,0,5,3,7,7,2
%N Digits of the 10-adic integer (17/9)^(1/3).
%H Seiichi Manyama, <a href="/A309600/b309600.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 - 17) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e 7^3 == 3 (mod 10).
%e 17^3 == 13 (mod 10^2).
%e 617^3 == 113 (mod 10^3).
%e 8617^3 == 1113 (mod 10^4).
%e 78617^3 == 11113 (mod 10^5).
%e 78617^3 == 111113 (mod 10^6).
%o (PARI) N=100; Vecrev(digits(lift(chinese(Mod((17/9+O(2^N))^(1/3), 2^N), Mod((17/9+O(5^N))^(1/3), 5^N)))), N)
%o (Ruby)
%o def A309600(n)
%o ary = [7]
%o a = 7
%o n.times{|i|
%o b = (a + 3 * (9 * a ** 3 - 17)) % (10 ** (i + 2))
%o ary << (b - a) / (10 ** (i + 1))
%o a = b
%o }
%o ary
%o end
%o p A309600(100)
%Y 10-adic integer x.
%Y A225404 (x^3 = ...000003).
%Y A225405 (x^3 = ...000007).
%Y A225406 (x^3 = ...000009).
%Y A153042 (x^3 = ...111111).
%Y this sequence (x^3 = ...111113).
%Y A309601 (x^3 = ...111117).
%Y A309602 (x^3 = ...111119).
%Y A309603 (x^3 = ...222221).
%Y A225410 (x^3 = ...222223).
%Y A309604 (x^3 = ...222227).
%Y A309605 (x^3 = ...222229).
%Y A309606 (x^3 = ...333331).
%Y A225402 (x^3 = ...333333).
%Y A309569 (x^3 = ...333337).
%Y A309570 (x^3 = ...333339).
%Y A309595 (x^3 = ...444441).
%Y A309608 (x^3 = ...444443).
%Y A309609 (x^3 = ...444447).
%Y A309610 (x^3 = ...444449).
%Y A309611 (x^3 = ...555551).
%Y A309612 (x^3 = ...555553).
%Y A309613 (x^3 = ...555557).
%Y A309614 (x^3 = ...555559).
%Y A309640 (x^3 = ...666661).
%Y A309641 (x^3 = ...666663).
%Y A225411 (x^3 = ...666667).
%Y A309642 (x^3 = ...666669).
%Y A309643 (x^3 = ...777771).
%Y A309644 (x^3 = ...777773).
%Y A225401 (x^3 = ...777777).
%Y A309645 (x^3 = ...777779).
%Y A309646 (x^3 = ...888881).
%Y A309647 (x^3 = ...888883).
%Y A309648 (x^3 = ...888887).
%Y A225412 (x^3 = ...888889).
%Y A225409 (x^3 = ...999991).
%Y A225408 (x^3 = ...999993).
%Y A225407 (x^3 = ...999997).
%K nonn,base
%O 0,1
%A _Seiichi Manyama_, Aug 09 2019