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%I #15 Aug 12 2019 02:39:37
%S 9,8,9,5,3,2,3,2,4,1,6,2,9,4,0,2,1,9,1,1,8,3,0,8,2,5,0,7,5,0,5,2,5,3,
%T 6,7,4,5,2,9,9,0,0,7,2,2,4,5,9,7,0,1,7,6,9,4,0,1,7,0,7,0,6,9,8,1,5,9,
%U 7,0,8,2,8,6,8,0,4,1,8,7,5,9,6,4,7,2,7,6,4,4,4,3,4,0,0,5,8,8,9,0
%N Digits of the 10-adic integer (7/3)^(1/3).
%H Seiichi Manyama, <a href="/A309642/b309642.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 - 7 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e 9^3 == 9 (mod 10).
%e 89^3 == 69 (mod 10^2).
%e 989^3 == 669 (mod 10^3).
%e 5989^3 == 6669 (mod 10^4).
%e 35989^3 == 66669 (mod 10^5).
%e 235989^3 == 666669 (mod 10^6).
%o (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 (Ruby)
%o def A309642(n)
%o ary = [9]
%o a = 9
%o n.times{|i|
%o b = (a + 3 * a ** 3 - 7) % (10 ** (i + 2))
%o ary << (b - a) / (10 ** (i + 1))
%o a = b
%o }
%o ary
%o end
%o p A309642(100)
%Y Cf. A309600, A309606.
%K nonn
%O 0,1
%A _Seiichi Manyama_, Aug 11 2019
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