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 A309724 Digits of the 8-adic integer (1/7)^(1/7). 3
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Wikipedia, Hensel's Lemma. FORMULA 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. PROG (PARI) N=100; Vecrev(digits(lift((1/7+O(2^(3*N)))^(1/7)), 8), N) (Ruby) def A309724(n)   ary = [7]   a = 7   n.times{|i|     b = (a + 7 * (7 * a ** 7 - 1)) % (8 ** (i + 2))     ary << (b - a) / (8 ** (i + 1))     a = b   }   ary end p A309724(100) CROSSREFS 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). Cf. A309700. Sequence in context: A137915 A316167 A272037 * A198114 A293384 A193012 Adjacent sequences:  A309721 A309722 A309723 * A309725 A309726 A309727 KEYWORD nonn,base AUTHOR Seiichi Manyama, Aug 14 2019 STATUS approved

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Last modified October 1 00:54 EDT 2020. Contains 337440 sequences. (Running on oeis4.)