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 A309699 Digits of the 6-adic integer 5^(1/5). 6
 5, 4, 0, 3, 1, 5, 0, 0, 3, 3, 2, 1, 3, 0, 0, 3, 4, 3, 1, 1, 1, 1, 1, 4, 3, 4, 0, 5, 3, 1, 1, 5, 3, 3, 0, 2, 2, 2, 5, 3, 5, 5, 2, 5, 2, 2, 2, 3, 4, 2, 0, 5, 4, 3, 3, 2, 0, 0, 4, 1, 1, 5, 5, 5, 0, 0, 1, 4, 3, 5, 4, 5, 1, 5, 5, 0, 5, 4, 0, 4, 4, 4, 4, 3, 4, 4, 0, 4, 3, 4, 0, 5, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS x = ...513045, x^2 = ...433521, x^3 = ...051525, x^4 = ...354241, x^5 = ...000005. 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) = 5, b(n) = b(n-1) + b(n-1)^5 - 5 mod 6^n for n > 1, then a(n) = (b(n+1) - b(n))/6^n. PROG (PARI) N=100; Vecrev(digits(lift(chinese(Mod((5+O(2^N))^(1/5), 2^N), Mod((5+O(3^N))^(1/5), 3^N))), 6), N) (Ruby) def A309699(n) ary = [5] a = 5 n.times{|i| b = (a + a ** 5 - 5) % (6 ** (i + 2)) ary << (b - a) / (6 ** (i + 1)) a = b } ary end p A309699(100) CROSSREFS Digits of the k-adic integer (k-1)^(1/(k-1)): A309698 (k=4), this sequence (k=6), A309700 (k=8), A225458 (k=10). Cf. A309448. Sequence in context: A185579 A197134 A049470 * A153106 A021189 A320411 Adjacent sequences: A309696 A309697 A309698 * A309700 A309701 A309702 KEYWORD nonn,base AUTHOR Seiichi Manyama, Aug 13 2019 STATUS approved

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Last modified March 4 16:59 EST 2024. Contains 370532 sequences. (Running on oeis4.)