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 A321108 Digits of one of the three 13-adic integers 5^(1/3) that is related to A321105. 13
 11, 11, 5, 11, 2, 0, 9, 0, 6, 11, 9, 6, 7, 9, 2, 9, 9, 2, 3, 3, 8, 2, 7, 11, 6, 7, 4, 7, 10, 5, 5, 4, 11, 6, 2, 5, 2, 7, 10, 9, 9, 2, 9, 5, 7, 7, 4, 5, 10, 4, 1, 6, 4, 1, 4, 0, 4, 10, 11, 4, 12, 12, 7, 2, 9, 6, 11, 8, 5, 6, 11, 2, 0, 6, 6, 12, 10, 8, 12, 11, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For k not divisible by 5, k is a cube in 13-adic field if and only if k == 1, 5, 8, 12 (mod 13). If k is a cube in 13-adic field, then k has exactly three cubic roots. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Wikipedia, p-adic number FORMULA a(n) = (A321105(n+1) - A321105(n))/13^n. EXAMPLE The unique number k in [1, 13^3] and congruent to 11 modulo 13 such that k^3 - 5 is divisible by 13^3 is k = 999 = (5BB)_13, so the first three terms are 11, 11 and 5. PROG (PARI) a(n) = lift(sqrtn(5+O(13^(n+1)), 3) * (-1-sqrt(-3+O(13^(n+1))))/2)\13^n CROSSREFS Cf. A320914, A320915, A321105, A321106, A321107. For 5-adic cubic roots, see A290566, A290563, A309443. Sequence in context: A135684 A220295 A300289 * A126610 A087380 A152986 Adjacent sequences:  A321105 A321106 A321107 * A321109 A321110 A321111 KEYWORD nonn,base AUTHOR Jianing Song, Aug 27 2019 STATUS approved

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Last modified September 28 08:36 EDT 2021. Contains 347713 sequences. (Running on oeis4.)