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A324023 One of the two successive approximations up to 5^n for 5-adic integer sqrt(6). This is the 1 (mod 5) case (except for n = 0).

%I A324023 #16 Sep 07 2019 18:04:39
%S A324023 0,1,16,16,516,1766,4891,36141,270516,661141,6520516,35817391,
%T A324023 35817391,768239266,4430348641,16637379891,108190114266,413365895516,
%U A324023 1939244801766,9568639333016,85862584645516,371964879567391,1802476354176766,4186662145192391,51870377965504891
%N A324023 One of the two successive approximations up to 5^n for 5-adic integer sqrt(6). This is the 1 (mod 5) case (except for n = 0).
%C A324023 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 A324023 A324024 is the approximation (congruent to 4 mod 5) of another square root of 6 over the 5-adic field.
%H A324023 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A324023 For n > 0, a(n) = 5^n - A324024(n).
%F A324023 a(n) = A048898(n)*A324028(n) mod 5^n = A048899(n)*A324027(n) mod 5^n.
%e A324023 16^2 = 256 = 10*5^2 + 6 = 2*5^3 + 6;
%e A324023 516^2 = 266256 = 426*5^4 + 6;
%e A324023 1766^2 = 3118756 = 998*5^5 + 6.
%o A324023 (PARI) a(n) = truncate(sqrt(6+O(5^n)))
%Y A324023 Cf. A048898, A048899, A324025, A324026.
%Y A324023 Approximations of 5-adic square roots:
%Y A324023 A324027, A324028 (sqrt(-6));
%Y A324023 A268922, A269590 (sqrt(-4));
%Y A324023 A048898, A048899 (sqrt(-1));
%Y A324023 this sequence, A324024 (sqrt(6)).
%K A324023 nonn
%O A324023 0,3
%A A324023 _Jianing Song_, Sep 07 2019