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A325489 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 1 mod 5.

%I A325489 #8 Sep 11 2019 20:35:55
%S A325489 1,4,4,1,3,1,3,3,1,0,2,2,2,2,0,3,4,3,0,4,2,1,2,2,0,1,1,2,4,2,3,4,2,1,
%T A325489 2,3,4,3,1,0,3,2,3,4,2,3,4,4,4,2,2,2,4,1,1,0,2,1,3,3,2,0,0,1,2,4,4,1,
%U A325489 0,4,1,0,2,4,0,2,2,0,1,3,1,1,4,3,4,1,2,2
%N A325489 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 1 mod 5.
%C A325489 One of the two square roots of A324025, where an A-number represents a 5-adic number. The other square root is A325492.
%C A325489 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 A325489 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A325489 Equals A325490*A210851 = A325491*A210850.
%F A325489 a(n) = (A325484(n+1) - A325484(n))/5^n.
%F A325489 For n > 0, a(n) = 4 - A325492(n).
%e A325489 The unique number k in [1, 5^3] and congruent to 1 modulo 5 such that k^4 - 6 is divisible by 5^3 is k = 121 = (441)_5, so the first three terms are 1, 4 and 4.
%o A325489 (PARI) a(n) = lift(sqrtn(6+O(5^(n+1)), 4))\5^n
%Y A325489 Cf. A210850, A210851, A324025, A325484, A325485, A325486, A325487.
%Y A325489 Digits of p-adic fourth-power roots:
%Y A325489 this sequence, A325490, A325491, A325492 (5-adic, 6^(1/4));
%Y A325489 A324085, A324086, A324087, A324153 (13-adic, 3^(1/4)).
%K A325489 nonn,base
%O A325489 0,2
%A A325489 _Jianing Song_, Sep 07 2019