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A322933 Digits of the 8-adic integer 7^(1/3).

%I A322933 #17 Aug 17 2019 03:13:56
%S A322933 7,2,6,6,2,7,7,2,0,6,5,6,7,3,5,6,1,5,6,1,0,0,2,4,6,1,5,0,4,3,3,4,3,3,
%T A322933 0,5,2,5,4,4,5,2,7,5,2,7,2,1,4,5,7,5,7,0,2,7,0,1,3,2,4,7,6,5,1,1,2,4,
%U A322933 2,0,7,2,5,4,0,4,7,0,4,3,5,5,1,3,4,4,6,1,7,7,3,5,3,6,6,5,7,5,0,6
%N A322933 Digits of the 8-adic integer 7^(1/3).
%C A322933 The octal version of A225405.
%H A322933 Seiichi Manyama, <a href="/A322933/b322933.txt">Table of n, a(n) for n = 0..10000</a>
%H A322933 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.
%F A322933 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 5 * (b(n-1)^3 - 7) mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n. - _Seiichi Manyama_, Aug 14 2019
%e A322933 56027726627^3 == 7 (mod 8^11) in octal.
%o A322933 (PARI) N=100; Vecrev(digits(lift((7+O(2^(3*N)))^(1/3)), 8), N) \\ _Seiichi Manyama_, Aug 14 2019
%o A322933 (Ruby)
%o A322933 def A322933(n)
%o A322933   ary = [7]
%o A322933   a = 7
%o A322933   n.times{|i|
%o A322933     b = (a + 5 * (a ** 3 - 7)) % (8 ** (i + 2))
%o A322933     ary << (b - a) / (8 ** (i + 1))
%o A322933     a = b
%o A322933   }
%o A322933   ary
%o A322933 end
%o A322933 p A322933(100) # _Seiichi Manyama_, Aug 14 2019
%Y A322933 Cf. A225405 (decimal version), A322931, A322932.
%K A322933 nonn,base,easy
%O A322933 0,1
%A A322933 _Patrick A. Thomas_, Dec 31 2018