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A325491 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 3 mod 5.

%I A325491 #8 Sep 11 2019 20:36:20
%S A325491 3,0,4,1,4,2,4,0,4,1,4,2,2,2,3,2,3,0,4,1,0,2,3,0,3,3,2,4,4,1,4,3,3,1,
%T A325491 3,0,0,4,2,0,4,0,3,2,4,3,2,1,2,0,2,0,3,1,4,2,3,4,1,1,1,1,4,2,2,1,3,3,
%U A325491 0,3,3,4,3,0,4,1,1,1,4,1,4,4,0,4,1,2,1,3
%N A325491 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 3 mod 5.
%C A325491 One of the two square roots of A324026, where an A-number represents a 5-adic number. The other square root is A325490.
%C A325491 For k not divisible by 5, k is a fourth power in 5-adic field if and only if k == 1 (mod 5). If k is a fourth power in 5-adic field, then k has exactly 4 fourth-power roots.
%H A325491 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A325491 Equals A325489*A210851 = A325492*A210850.
%F A325491 a(n) = (A325486(n+1) - A325486(n))/13^n.
%F A325491 For n > 0, a(n) = 4 - A325490(n).
%e A325491 The unique number k in [1, 5^3] and congruent to 3 modulo 5 such that k^4 - 6 is divisible by 5^3 is k = 103 = (403)_5, so the first three terms are 3, 0 and 4.
%o A325491 (PARI) a(n) = lift(-sqrtn(6+O(5^(n+1)), 4) * sqrt(-1+O(5^(n+1))))\5^n
%Y A325491 Cf. A210850, A210851, A324026, A325484, A325485, A325486, A325487.
%Y A325491 Digits of p-adic fourth-power roots:
%Y A325491 A325489, A325490, this sequence, A325492 (5-adic, 6^(1/4));
%Y A325491 A324085, A324086, A324087, A324153 (13-adic, 3^(1/4)).
%K A325491 nonn,base
%O A325491 0,1
%A A325491 _Jianing Song_, Sep 07 2019