cp's OEIS Frontend

A324027 One of the two successive approximations up to 5^n for 5-adic integer sqrt(-6). This is the 2 (mod 5) case (except for n = 0).

%I A324027 #14 Sep 07 2019 18:05:03
%S A324027 0,2,12,37,162,1412,10787,42037,354537,1526412,3479537,3479537,
%T A324027 3479537,247620162,3909729537,10013245162,101565979537,711917542037,
%U A324027 2237796448287,13681888245162,51828860901412,337931155823287,1291605472229537,10828348636292037,58512064456604537
%N A324027 One of the two successive approximations up to 5^n for 5-adic integer sqrt(-6). This is the 2 (mod 5) case (except for n = 0).
%C A324027 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 2 modulo 5.
%C A324027 A324028 is the approximation (congruent to 3 mod 5) of another square root of 6 over the 5-adic field.
%H A324027 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A324027 For n > 0, a(n) = 5^n - A324028(n).
%F A324027 a(n) = A048898(n)*A324023(n) mod 5^n = A048899(n)*A324024(n) mod 5^n.
%e A324027 12^2 = 144 = 6*5^2 - 6;
%e A324027 37^2 = 1369 = 11*5^3 - 6;
%e A324027 162^2 = 26244 = 42*5^4 - 6.
%o A324027 (PARI) a(n) = truncate(sqrt(-6+O(5^n)))
%Y A324027 Cf. A048898, A048899, A324029, A324030.
%Y A324027 Approximations of 5-adic square roots:
%Y A324027 this sequence, A324028 (sqrt(-6));
%Y A324027 A268922, A269590 (sqrt(-4));
%Y A324027 A048898, A048899 (sqrt(-1));
%Y A324027 A324023, A324024 (sqrt(6)).
%K A324027 nonn
%O A324027 0,2
%A A324027 _Jianing Song_, Sep 07 2019