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A318962 Digits of one of the two 2-adic integers sqrt(-7) that ends in 01.

%I A318962 #36 Feb 19 2021 09:47:01
%S A318962 1,0,1,0,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,
%T A318962 0,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,1,
%U A318962 1,1,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,1
%N A318962 Digits of one of the two 2-adic integers sqrt(-7) that ends in 01.
%C A318962 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 former one. See A318960 for detailed information.
%H A318962 Jianing Song, <a href="/A318962/b318962.txt">Table of n, a(n) for n = 0..1000</a>
%F A318962 a(0) = 1, a(1) = 0; for n >= 2, a(n) = 0 if A318960(n)^2 + 7 is divisible by 2^(n+2), otherwise 1.
%F A318962 a(n) = 1 - A318963(n) for n >= 1.
%F A318962 For n >= 2, a(n) = (A318960(n+1) - A318960(n))/2^n.
%e A318962 ...10110001110011100100110001100000010110101.
%o A318962 (PARI) a(n) = truncate(-sqrt(-7+O(2^(n+2))))\2^n
%Y A318962 Cf. A318960.
%Y A318962 Digits of p-adic integers:
%Y A318962 this sequence, A318963 (2-adic, sqrt(-7));
%Y A318962 A271223, A271224 (3-adic, sqrt(-2));
%Y A318962 A269591, A269592 (5-adic, sqrt(-4));
%Y A318962 A210850, A210851 (5-adic, sqrt(-1));
%Y A318962 A290566 (5-adic, 2^(1/3));
%Y A318962 A290563 (5-adic, 3^(1/3));
%Y A318962 A290794, A290795 (7-adic, sqrt(-6));
%Y A318962 A290798, A290799 (7-adic, sqrt(-5));
%Y A318962 A290796, A290797 (7-adic, sqrt(-3));
%Y A318962 A212152, A212155 (7-adic, (1+sqrt(-3))/2);
%Y A318962 A051277, A290558 (7-adic, sqrt(2));
%Y A318962 A286838, A286839 (13-adic, sqrt(-1));
%Y A318962 A309989, A309990 (17-adic, sqrt(-1)).
%Y A318962 Also there are numerous sequences related to digits of 10-adic integers.
%K A318962 nonn,base
%O A318962 0,1
%A A318962 _Jianing Song_, Sep 06 2018
%E A318962 Corrected by _Jianing Song_, Aug 28 2019