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 A324085 Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 2 mod 13. 13
 2, 2, 7, 1, 12, 6, 12, 4, 8, 6, 1, 10, 4, 6, 7, 8, 10, 1, 12, 9, 9, 7, 0, 12, 3, 6, 4, 5, 11, 12, 3, 11, 9, 5, 8, 4, 4, 2, 7, 4, 11, 8, 4, 10, 1, 0, 2, 1, 4, 3, 11, 7, 3, 6, 3, 2, 6, 7, 3, 6, 1, 0, 3, 0, 11, 8, 11, 6, 11, 0, 3, 5, 4, 7, 9, 10, 12, 6, 11, 5, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS One of the two square roots of A322087, where an A-number represents a 13-adic number. The other square root is A324153. For k not divisible by 13, k is a fourth power in 13-adic field if and only if k == 1, 3, 9 (mod 13). If k is a fourth power in 13-adic field, then k has exactly 4 fourth-power roots. LINKS Wikipedia, p-adic number FORMULA Equals A324086*A286838 = A324087*A286839. a(n) = (A324077(n+1) - A324077(n))/13^n. For n > 0, a(n) = 12 - A324153(n). EXAMPLE The unique number k in [1, 13^3] and congruent to 2 modulo 13 such that k^4 - 3 is divisible by 13^3 is k = 1211 = (722)_13, so the first three terms are 2, 7 and 7. PROG (PARI) a(n) = lift(sqrtn(3+O(13^(n+1)), 4) * sqrt(-1+O(13^(n+1))))\13^n CROSSREFS Cf. A286838, A286839, A322087, A324077, A324082, A324083, A324084, A324086, A324087, A324153. Sequence in context: A190256 A013671 A019807 * A340180 A063706 A110779 Adjacent sequences:  A324082 A324083 A324084 * A324086 A324087 A324088 KEYWORD nonn,base AUTHOR Jianing Song, Sep 01 2019 STATUS approved

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Last modified April 14 18:16 EDT 2021. Contains 342951 sequences. (Running on oeis4.)