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A324029 Digits of one of the two 5-adic integers sqrt(-6) that is related to A324027.

%I A324029 #18 Mar 11 2023 07:56:09
%S A324029 2,2,1,1,2,3,2,4,3,1,0,0,1,3,1,3,4,2,3,2,3,2,4,4,2,3,3,0,1,1,3,1,1,1,
%T A324029 3,1,2,3,2,3,4,1,0,2,4,4,3,4,0,3,2,0,2,0,2,0,3,2,0,0,4,2,4,4,0,4,4,4,
%U A324029 3,1,4,2,2,4,2,0,0,0,3,0,4,3,2,4,3,3,4,0
%N A324029 Digits of one of the two 5-adic integers sqrt(-6) that is related to A324027.
%C A324029 This square root of -6 in the 5-adic field ends with digit 2. The other, A324030, ends with digit 3.
%H A324029 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A324029 a(n) = (A324027(n+1) - A324027(n))/5^n.
%F A324029 For n > 0, a(n) = 4 - A324030(n).
%F A324029 Equals A210850*A324026 = A210851*A324025, where each A-number represents a 5-adic number.
%e A324029 The solution to x^2 == -6 (mod 5^4) such that x == 2 (mod 5) is x == 162 (mod 5^4), and 162 is written as 1122 in quinary, so the first four terms are 2, 2, 1 and 1.
%o A324029 (PARI) a(n) = truncate(sqrt(-6+O(5^(n+1))))\5^n
%Y A324029 Cf. A324027, A324028.
%Y A324029 Digits of 5-adic square roots:
%Y A324029 this sequence, A324030 (sqrt(-6));
%Y A324029 A269591, A269592 (sqrt(-4));
%Y A324029 A210850, A210851 (sqrt(-1));
%Y A324029 A324025, A324026 (sqrt(6)).
%K A324029 nonn,base
%O A324029 0,1
%A A324029 _Jianing Song_, Sep 07 2019