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 A324087 Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 10 mod 13. 11
 10, 7, 9, 6, 7, 0, 2, 10, 0, 0, 4, 0, 1, 5, 12, 10, 7, 1, 1, 9, 7, 1, 7, 8, 0, 0, 9, 10, 5, 5, 0, 1, 4, 7, 0, 9, 7, 4, 6, 0, 3, 8, 12, 7, 7, 0, 11, 3, 11, 3, 1, 5, 8, 12, 9, 3, 12, 0, 6, 6, 11, 4, 8, 3, 7, 6, 3, 7, 5, 2, 11, 9, 9, 4, 7, 1, 4, 10, 12, 11, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS One of the two square roots of A322088, where an A-number represents a 13-adic number. The other square root is A324086. 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 A324085*A286838 = A324153*A286839. a(n) = (A324083(n+1) - A324083(n))/13^n. For n > 0, a(n) = 12 - A324086(n). EXAMPLE The unique number k in [1, 13^3] and congruent to 10 modulo 13 such that k^4 - 3 is divisible by 13^3 is k = 1622 = (97A)_13, so the first three terms are 10, 7 and 9. PROG (PARI) a(n) = lift(-sqrtn(3+O(13^(n+1)), 4))\13^n CROSSREFS Cf. A286838, A286839, A322087, A324077, A324082, A324083, A324084, A324085, A324086, A324153. Sequence in context: A089245 A098592 A016731 * A068444 A210285 A190996 Adjacent sequences:  A324084 A324085 A324086 * A324088 A324089 A324090 KEYWORD nonn,base AUTHOR Jianing Song, Sep 01 2019 STATUS approved

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)