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A324024 One of the two successive approximations up to 5^n for 5-adic integer sqrt(6). This is the 4 (mod 5) case (except for n = 0).

%I A324024 #14 Sep 07 2019 18:04:57
%S A324024 0,4,9,109,109,1359,10734,41984,120109,1291984,3245109,13010734,
%T A324024 208323234,452463859,1673166984,13880198234,44397776359,349573557609,
%U A324024 1875452463859,9504846995109,9504846995109,104872278635734,581709436838859,7734266809885734,7734266809885734
%N A324024 One of the two successive approximations up to 5^n for 5-adic integer sqrt(6). This is the 4 (mod 5) case (except for n = 0).
%C A324024 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 1 modulo 5.
%C A324024 A324023 is the approximation (congruent to 4 mod 5) of another square root of 6 over the 5-adic field.
%H A324024 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A324024 For n > 0, a(n) = 5^n - A324023(n).
%F A324024 a(n) = A048898(n)*A324027(n) mod 5^n = A048899(n)*A324028(n) mod 5^n.
%e A324024 9^2 = 81 = 3*5^2 + 6;
%e A324024 109^2 = 11881 = 95*5^3 + 6 = 19*5^4 + 6;
%e A324024 1359^2 = 1846881 = 591*5^5 + 6.
%o A324024 (PARI) a(n) = truncate(-sqrt(6+O(5^n)))
%Y A324024 Cf. A048898, A048899, A324025, A324026.
%Y A324024 Approximations of 5-adic square roots:
%Y A324024 A324027, A324028 (sqrt(-6));
%Y A324024 A268922, A269590 (sqrt(-4));
%Y A324024 A048898, A048899 (sqrt(-1));
%Y A324024 A324023, this sequence (sqrt(6)).
%K A324024 nonn
%O A324024 0,2
%A A324024 _Jianing Song_, Sep 07 2019