A325492 - OEIS

%I #8 Sep 11 2019 20:36:30

%S 4,0,0,3,1,3,1,1,3,4,2,2,2,2,4,1,0,1,4,0,2,3,2,2,4,3,3,2,0,2,1,0,2,3,

%T 2,1,0,1,3,4,1,2,1,0,2,1,0,0,0,2,2,2,0,3,3,4,2,3,1,1,2,4,4,3,2,0,0,3,

%U 4,0,3,4,2,0,4,2,2,4,3,1,3,3,0,1,0,3,2,2

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

%C One of the two square roots of A324025, where an A-number represents a 5-adic number. The other square root is A325489.

%C 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>

%F Equals A325490*A210850 = A325491*A210851.

%F a(n) = (A325487(n+1) - A325487(n))/5^n.

%F For n > 0, a(n) = 4 - A325489(n).

%e The unique number k in [1, 5^3] and congruent to 4 modulo 5 such that k^4 - 6 is divisible by 5^3 is k = 4 = (4)_5, so the first three terms are 4, 0 and 0.

%o (PARI) a(n) = lift(-sqrtn(6+O(5^(n+1)), 4))\5^n

%Y Cf. A210850, A210851, A324025, A325484, A325485, A325486, A325487.

%Y Digits of p-adic fourth-power roots:

%Y A325489, A325490, A325491, this sequence (5-adic, 6^(1/4));

%Y A324085, A324086, A324087, A324153 (13-adic, 3^(1/4)).

%K nonn,base

%O 0,1

%A _Jianing Song_, Sep 07 2019