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A324026 Digits of one of the two 5-adic integers sqrt(6) that is related to A324024.

%I A324026 #18 Mar 11 2023 07:55:59
%S A324026 4,1,4,0,2,3,2,1,3,1,1,4,1,1,2,1,2,2,2,0,1,1,3,0,4,3,2,4,4,4,1,1,3,0,
%T A324026 3,4,3,2,0,3,0,3,3,4,2,0,0,1,4,2,1,0,3,3,0,1,0,2,0,2,3,3,2,0,0,1,2,1,
%U A324026 3,3,4,3,0,2,1,0,0,0,0,4,1,1,3,2,1,2,1,3
%N A324026 Digits of one of the two 5-adic integers sqrt(6) that is related to A324024.
%C A324026 This square root of 6 in the 5-adic field ends with digit 4. The other, A324025, ends with digit 1.
%H A324026 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A324026 a(n) = (A324024(n+1) - A324024(n))/5^n.
%F A324026 For n > 0, a(n) = 4 - A324025(n).
%F A324026 Equals A210850*A324029 = A210851*A324030, where each A-number represents a 5-adic number.
%e A324026 The solution to x^2 == 6 (mod 5^4) such that x == 4 (mod 5) is x == 109 (mod 5^4), and 109 is written as 414 in quinary, so the first four terms are 4, 1, 4 and 0.
%o A324026 (PARI) a(n) = truncate(-sqrt(6+O(5^(n+1))))\5^n
%Y A324026 Cf. A324023, A324024.
%Y A324026 Digits of 5-adic square roots:
%Y A324026 A324029, A324030 (sqrt(-6));
%Y A324026 A269591, A269592 (sqrt(-4));
%Y A324026 A210850, A210851 (sqrt(-1));
%Y A324026 A324025, this sequence (sqrt(6)).
%K A324026 nonn,base
%O A324026 0,1
%A A324026 _Jianing Song_, Sep 07 2019