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A324028 One of the two successive approximations up to 5^n for 5-adic integer sqrt(-6). This is the 3 (mod 5) case (except for n = 0).

%I A324028 #14 Sep 07 2019 18:05:12
%S A324028 0,3,13,88,463,1713,4838,36088,36088,426713,6286088,45348588,
%T A324028 240661088,973082963,2193786088,20504332963,51021911088,51021911088,
%U A324028 1576900817338,5391598082963,43538570739213,138906002379838,1092580318786088,1092580318786088,1092580318786088
%N A324028 One of the two successive approximations up to 5^n for 5-adic integer sqrt(-6). This is the 3 (mod 5) case (except for n = 0).
%C A324028 For n > 0, a(n) is the unique solution to x^2 == -6 (mod 5^n) in the range [0, 5^n - 1] and congruent to 3 modulo 5.
%C A324028 A324027 is the approximation (congruent to 3 mod 5) of another square root of -6 over the 5-adic field.
%H A324028 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A324028 For n > 0, a(n) = 5^n - A324027(n).
%F A324028 a(n) = A048898(n)*A324024(n) mod 5^n = A048899(n)*A324023(n) mod 5^n.
%e A324028 13^2 = 169 = 7*5^2 - 6;
%e A324028 88^2 = 7744 = 62*5^3 - 6;
%e A324028 463^2 = 214369 = 343*5^4 - 6.
%o A324028 (PARI) a(n) = truncate(-sqrt(-6+O(5^n)))
%Y A324028 Cf. A048898, A048899, A324029, A324030.
%Y A324028 Approximations of 5-adic square roots:
%Y A324028 A324027, sequence (sqrt(-6));
%Y A324028 A268922, A269590 (sqrt(-4));
%Y A324028 A048898, A048899 (sqrt(-1));
%Y A324028 A324023, A324024 (sqrt(6)).
%K A324028 nonn
%O A324028 0,2
%A A324028 _Jianing Song_, Sep 07 2019