A341540 - OEIS

%I #16 Feb 18 2021 02:53:46

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

%T 1,1,0,0,0,0,0,1,1,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,1,0,0,

%U 0,1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,1,1,0,1,1,1,1

%N Expansion of the 2-adic integer sqrt(17) that ends in 11.

%C Over the 2-adic integers there are 2 solutions to x^2 = 17, one ends in 01 and the other ends in 11. This sequence gives the latter one. See A341539 for detailed information.

%H Jianing Song, <a href="/A341540/b341540.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 A341539(n)^2 - 17 is divisible by 2^(n+2), otherwise 1.

%F a(n) = 1 - A322217(n) for n >= 1.

%F For n >= 2, a(n) = (A341539(n+1) - A341539(n))/2^n.

%e If x = ...00000110011001100001011001101100100010111, then x^2 = 10001_2 = 17.

%o (PARI) a(n) = if(n==1, 1, truncate(-sqrt(17+O(2^(n+2))))\2^n)

%Y Cf. A322217, A341539 (successive approximations of the associated 2-adic square root of 17), A318962, A318963 (expansion of sqrt(-7)).

%K nonn,base

%O 0

%A _Jianing Song_, Feb 13 2021