A324028 - OEIS

%I #14 Sep 07 2019 18:05:12

%S 0,3,13,88,463,1713,4838,36088,36088,426713,6286088,45348588,

%T 240661088,973082963,2193786088,20504332963,51021911088,51021911088,

%U 1576900817338,5391598082963,43538570739213,138906002379838,1092580318786088,1092580318786088,1092580318786088

%N 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 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 A324027 is the approximation (congruent to 3 mod 5) of another square root of -6 over the 5-adic field.

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

%F For n > 0, a(n) = 5^n - A324027(n).

%F a(n) = A048898(n)*A324024(n) mod 5^n = A048899(n)*A324023(n) mod 5^n.

%e 13^2 = 169 = 7*5^2 - 6;

%e 88^2 = 7744 = 62*5^3 - 6;

%e 463^2 = 214369 = 343*5^4 - 6.

%o (PARI) a(n) = truncate(-sqrt(-6+O(5^n)))

%Y Cf. A048898, A048899, A324029, A324030.

%Y Approximations of 5-adic square roots:

%Y A324027, sequence (sqrt(-6));

%Y A268922, A269590 (sqrt(-4));

%Y A048898, A048899 (sqrt(-1));

%Y A324023, A324024 (sqrt(6)).

%K nonn

%O 0,2

%A _Jianing Song_, Sep 07 2019