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A324030 Digits of one of the two 5-adic integers sqrt(-6) that is related to A324028.

%I A324030 #19 Mar 11 2023 07:56:17
%S A324030 3,2,3,3,2,1,2,0,1,3,4,4,3,1,3,1,0,2,1,2,1,2,0,0,2,1,1,4,3,3,1,3,3,3,
%T A324030 1,3,2,1,2,1,0,3,4,2,0,0,1,0,4,1,2,4,2,4,2,4,1,2,4,4,0,2,0,0,4,0,0,0,
%U A324030 1,3,0,2,2,0,2,4,4,4,1,4,0,1,2,0,1,1,0,4
%N A324030 Digits of one of the two 5-adic integers sqrt(-6) that is related to A324028.
%C A324030 This square root of -6 in the 5-adic field ends with digit 3. The other, A324029, ends with digit 2.
%H A324030 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A324030 a(n) = (A324028(n+1) - A324028(n))/5^n.
%F A324030 For n > 0, a(n) = 4 - A324029(n).
%F A324030 Equals A210850*A324025 = A210851*A324026, where each A-number represents a 5-adic number.
%e A324030 The solution to x^2 == -6 (mod 5^4) such that x == 3 (mod 5) is x == 463 (mod 5^4), and 463 is written as 3323 in quinary, so the first four terms are 3, 2, 3 and 3.
%o A324030 (PARI) a(n) = truncate(-sqrt(-6+O(5^(n+1))))\5^n
%Y A324030 Cf. A324027, A324028.
%Y A324030 Digits of 5-adic square roots:
%Y A324030 A324029, sequence (sqrt(-6));
%Y A324030 A269591, A269592 (sqrt(-4));
%Y A324030 A210850, A210851 (sqrt(-1));
%Y A324030 A324025, A324026 (sqrt(6)).
%K A324030 nonn,base
%O A324030 0,1
%A A324030 _Jianing Song_, Sep 07 2019