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 A309722 Digits of the 4-adic integer (1/3)^(1/3). 3
 3, 0, 3, 2, 1, 1, 0, 1, 2, 2, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 2, 3, 2, 2, 3, 2, 3, 3, 1, 1, 2, 0, 1, 3, 0, 0, 2, 3, 2, 2, 2, 0, 0, 0, 0, 0, 3, 2, 0, 2, 0, 2, 0, 0, 2, 3, 2, 3, 2, 2, 3, 3, 2, 2, 2, 0, 2, 3, 1, 0, 0, 3, 3, 2, 3, 3, 3, 0, 3, 1, 3, 2, 3, 2, 2, 1, 2, 0, 3, 2, 0, 2, 3, 0, 0, 2, 0, 3, 3, 0 (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) = 3, b(n) = b(n-1) + 3 * (3 * b(n-1)^3 - 1) mod 4^n for n > 1, then a(n) = (b(n+1) - b(n))/4^n. PROG (PARI) N=100; Vecrev(digits(lift((1/3+O(2^(2*N)))^(1/3)), 4), N) (Ruby) def A309722(n)   ary = [3]   a = 3   n.times{|i|     b = (a + 3 * (3 * a ** 3 - 1)) % (4 ** (i + 2))     ary << (b - a) / (4 ** (i + 1))     a = b   }   ary end p A309722(100) CROSSREFS Digits of the k-adic integer (1/(k-1))^(1/(k-1)): this sequence (k=4), A309723 (k=6), A309724 (k=8), A225464 (k=10). Cf. A225411, A309698. Sequence in context: A171911 A180193 A229964 * A070298 A024938 A332715 Adjacent sequences:  A309719 A309720 A309721 * A309723 A309724 A309725 KEYWORD nonn,base AUTHOR Seiichi Manyama, Aug 14 2019 STATUS approved

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Last modified April 14 15:18 EDT 2021. Contains 342949 sequences. (Running on oeis4.)