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A324086 Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 3 mod 13.

%I A324086 #8 Sep 07 2019 19:09:33
%S A324086 3,5,3,6,5,12,10,2,12,12,8,12,11,7,0,2,5,11,11,3,5,11,5,4,12,12,3,2,7,
%T A324086 7,12,11,8,5,12,3,5,8,6,12,9,4,0,5,5,12,1,9,1,9,11,7,4,0,3,9,0,12,6,6,
%U A324086 1,8,4,9,5,6,9,5,7,10,1,3,3,8,5,11,8,2,0,1,12
%N A324086 Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 3 mod 13.
%C A324086 One of the two square roots of A322088, where an A-number represents a 13-adic number. The other square root is A324087.
%C 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.
%H A324086 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A324086 Equals A324085*A286839 = A324153*A286838.
%F A324086 a(n) = (A324082(n+1) - A324082(n))/13^n.
%F A324086 For n > 0, a(n) = 12 - A324087(n).
%e A324086 The unique number k in [1, 13^3] and congruent to 3 modulo 13 such that k^4 - 3 is divisible by 13^3 is k = 575 = (353)_13, so the first three terms are 3, 5 and 3.
%o A324086 (PARI) a(n) = lift(sqrtn(3+O(13^(n+1)), 4))\13^n
%Y A324086 Cf. A286838, A286839, A322087, A324077, A324082, A324083, A324084, A324085, A324087, A324153.
%K A324086 nonn,base
%O A324086 0,1
%A A324086 _Jianing Song_, Sep 01 2019