cp's OEIS Frontend

A309724 Digits of the 8-adic integer (1/7)^(1/7).

%I A309724 #17 Aug 17 2019 05:06:45
%S A309724 7,0,5,4,4,7,7,4,1,6,1,3,3,0,3,4,5,0,5,4,2,7,5,3,1,4,7,6,0,6,1,2,4,6,
%T A309724 2,2,1,6,2,0,2,5,1,6,3,4,0,6,1,2,4,0,5,6,5,5,0,4,6,7,5,4,0,0,1,6,3,6,
%U A309724 7,6,1,2,7,2,3,3,7,1,5,5,4,6,3,4,6,1,3,3,3,2,6,1,4,3,0,0,1,4,4,5,4
%N A309724 Digits of the 8-adic integer (1/7)^(1/7).
%H A309724 Seiichi Manyama, <a href="/A309724/b309724.txt">Table of n, a(n) for n = 0..10000</a>
%H A309724 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.
%F A309724 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 7 * (7 * b(n-1)^7 - 1) mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n.
%o A309724 (PARI) N=100; Vecrev(digits(lift((1/7+O(2^(3*N)))^(1/7)), 8), N)
%o A309724 (Ruby)
%o A309724 def A309724(n)
%o A309724   ary = [7]
%o A309724   a = 7
%o A309724   n.times{|i|
%o A309724     b = (a + 7 * (7 * a ** 7 - 1)) % (8 ** (i + 2))
%o A309724     ary << (b - a) / (8 ** (i + 1))
%o A309724     a = b
%o A309724   }
%o A309724   ary
%o A309724 end
%o A309724 p A309724(100)
%Y A309724 Digits of the k-adic integer (1/(k-1))^(1/(k-1)): A309722 (k=4), A309723 (k=6), this sequence (k=8), A225464 (k=10).
%Y A309724 Cf. A309700.
%K A309724 nonn,base
%O A309724 0,1
%A A309724 _Seiichi Manyama_, Aug 14 2019