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A318963 Digits of one of the two 2-adic integers sqrt(-7) that ends in 11.

%I A318963 #34 Feb 18 2021 21:12:58
%S A318963 1,1,0,1,0,0,1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,
%T A318963 1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,
%U A318963 0,0,1,1,1,0,1,1,0,1,0,1,1,1,1,1,1,1,0
%N A318963 Digits of one of the two 2-adic integers sqrt(-7) that ends in 11.
%C A318963 Over the 2-adic integers there are 2 solutions to x^2 = -7, one ends in 01 and the other ends in 11. This sequence gives the latter one. See A318961 for detailed information.
%H A318963 Jianing Song, <a href="/A318963/b318963.txt">Table of n, a(n) for n = 0..1000</a>
%F A318963 a(0) = a(1) = 1; for n >= 2, a(n) = 0 if A318961(n)^2 + 7 is divisible by 2^(n+2), otherwise 1.
%F A318963 a(n) = 1 - A318962(n) for n >= 1.
%F A318963 For n >= 2, a(n) = (A318961(n+1) - A318961(n))/2^n.
%e A318963 ...01001110001100011011001110011111101001011.
%o A318963 (PARI) a(n) = if(n==1, 1, truncate(sqrt(-7+O(2^(n+2))))\2^n)
%Y A318963 Cf. A318961.
%Y A318963 Digits of p-adic integers:
%Y A318963 A318962, this sequence (2-adic, sqrt(-7));
%Y A318963 A271223, A271224 (3-adic, sqrt(-2));
%Y A318963 A269591, A269592 (5-adic, sqrt(-4));
%Y A318963 A210850, A210851 (5-adic, sqrt(-1));
%Y A318963 A290566 (5-adic, 2^(1/3));
%Y A318963 A290563 (5-adic, 3^(1/3));
%Y A318963 A290794, A290795 (7-adic, sqrt(-6));
%Y A318963 A290798, A290799 (7-adic, sqrt(-5));
%Y A318963 A290796, A290797 (7-adic, sqrt(-3));
%Y A318963 A212152, A212155 (7-adic, (1+sqrt(-3))/2);
%Y A318963 A051277, A290558 (7-adic, sqrt(2));
%Y A318963 A286838, A286839 (13-adic, sqrt(-1));
%Y A318963 A309989, A309990 (17-adic, sqrt(-1)).
%Y A318963 Also there are numerous sequences related to digits of 10-adic integers.
%K A318963 nonn,base
%O A318963 0,1
%A A318963 _Jianing Song_, Sep 06 2018
%E A318963 Corrected by _Jianing Song_, Aug 28 2019