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Digits of the 8-adic integer 7^(1/7).
5

%I #20 Aug 14 2019 08:32:03

%S 7,6,1,0,1,6,4,1,7,3,6,4,4,5,3,3,4,2,0,0,6,2,5,4,2,6,6,3,2,2,6,1,0,3,

%T 5,6,1,6,6,7,0,6,6,7,7,5,3,2,2,7,5,5,1,7,5,7,1,1,1,2,5,0,4,3,2,5,3,0,

%U 3,3,1,7,3,4,5,4,5,1,1,2,2,7,0,6,7,1,4,4,6,7,6,2,2,5

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

%H Seiichi Manyama, <a href="/A309700/b309700.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.

%F Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + b(n-1)^7 - 7 mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n.

%o (PARI) N=100; Vecrev(digits(lift((7+O(2^(3*N)))^(1/7)), 8), N)

%o (Ruby)

%o def A309700(n)

%o ary = [7]

%o a = 7

%o n.times{|i|

%o b = (a + a ** 7 - 7) % (8 ** (i + 2))

%o ary << (b - a) / (8 ** (i + 1))

%o a = b

%o }

%o ary

%o end

%o p A309700(100)

%Y Digits of the k-adic integer (k-1)^(1/(k-1)): A309698 (k=4), A309699 (k=6), this sequence (k=8), A225458 (k=10).

%Y Cf. A225445.

%K nonn,base

%O 0,1

%A _Seiichi Manyama_, Aug 13 2019