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Digits of one of the two 2-adic integers sqrt(-7) that ends in 01.
9

%I #36 Feb 19 2021 09:47:01

%S 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 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 1,1,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,1

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

%C 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 Jianing Song, <a href="/A318962/b318962.txt">Table of n, a(n) for n = 0..1000</a>

%F 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 a(n) = 1 - A318963(n) for n >= 1.

%F For n >= 2, a(n) = (A318960(n+1) - A318960(n))/2^n.

%e ...10110001110011100100110001100000010110101.

%o (PARI) a(n) = truncate(-sqrt(-7+O(2^(n+2))))\2^n

%Y Cf. A318960.

%Y Digits of p-adic integers:

%Y this sequence, A318963 (2-adic, sqrt(-7));

%Y A271223, A271224 (3-adic, sqrt(-2));

%Y A269591, A269592 (5-adic, sqrt(-4));

%Y A210850, A210851 (5-adic, sqrt(-1));

%Y A290566 (5-adic, 2^(1/3));

%Y A290563 (5-adic, 3^(1/3));

%Y A290794, A290795 (7-adic, sqrt(-6));

%Y A290798, A290799 (7-adic, sqrt(-5));

%Y A290796, A290797 (7-adic, sqrt(-3));

%Y A212152, A212155 (7-adic, (1+sqrt(-3))/2);

%Y A051277, A290558 (7-adic, sqrt(2));

%Y A286838, A286839 (13-adic, sqrt(-1));

%Y A309989, A309990 (17-adic, sqrt(-1)).

%Y Also there are numerous sequences related to digits of 10-adic integers.

%K nonn,base

%O 0,1

%A _Jianing Song_, Sep 06 2018

%E Corrected by _Jianing Song_, Aug 28 2019