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A322932 Digits of the 8-adic integer 5^(1/3).

%I A322932 #15 Aug 14 2019 08:33:21
%S A322932 5,3,1,7,4,4,0,2,3,3,6,0,6,7,6,7,5,4,0,5,3,2,2,2,4,6,2,6,1,0,6,2,7,4,
%T A322932 3,3,7,4,3,7,5,6,4,5,1,3,3,0,1,7,4,4,7,0,7,5,3,2,1,5,1,5,6,1,1,0,1,6,
%U A322932 1,4,7,4,0,1,1,5,6,0,6,3,5,0,3,4,0,3,5,1,3,5,3,4,0,3,4,7,4,2,6,0
%N A322932 Digits of the 8-adic integer 5^(1/3).
%H A322932 Seiichi Manyama, <a href="/A322932/b322932.txt">Table of n, a(n) for n = 0..10000</a>
%H A322932 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.
%F A322932 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 5, b(n) = b(n-1) + 5 * (b(n-1)^3 - 5) mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n. - _Seiichi Manyama_, Aug 14 2019
%e A322932 20447135^3 == 5 (mod 8^8) in octal.
%o A322932 (PARI) N=100; Vecrev(digits(lift((5+O(2^(3*N)))^(1/3)), 8), N) \\ _Seiichi Manyama_, Aug 14 2019
%o A322932 (Ruby)
%o A322932 def A322932(n)
%o A322932   ary = [5]
%o A322932   a = 5
%o A322932   n.times{|i|
%o A322932     b = (a + 5 * (a ** 3 - 5)) % (8 ** (i + 2))
%o A322932     ary << (b - a) / (8 ** (i + 1))
%o A322932     a = b
%o A322932   }
%o A322932   ary
%o A322932 end
%o A322932 p A322932(100) # _Seiichi Manyama_, Aug 14 2019
%Y A322932 Cf. A322931, A322933.
%K A322932 nonn,base,easy
%O A322932 0,1
%A A322932 _Patrick A. Thomas_, Dec 31 2018