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A309474 Digits of one of the two 3-adic integers sqrt(-1/2). 3

%I #18 Aug 05 2019 15:30:48

%S 1,2,1,2,2,1,2,0,1,1,1,0,2,1,2,0,1,2,0,1,0,0,1,2,0,2,1,1,1,2,2,2,1,0,

%T 1,2,1,2,1,1,2,1,2,0,0,1,2,1,1,1,0,1,0,1,2,1,2,1,2,2,0,2,1,0,1,2,1,0,

%U 2,1,2,1,0,2,1,2,2,0,2,1,1,2,0,2,0,2,0,2,2,0,2,2,0,0,0,1,2

%N Digits of one of the two 3-adic integers sqrt(-1/2).

%H Robert Israel, <a href="/A309474/b309474.txt">Table of n, a(n) for n = 0..10000</a>

%F p = ...122121, p^2 = ...111111.

%F q = A271223 = ...200211, p * q = ...000001.

%F a(n) = (b(n+1) - b(n))/3^n, with b(n) = A309476(n).

%p T:= select(t -> padic:-ratvaluep(t,1)=1, [padic:-rootp(x^2+1/2,3,100)]):

%p op([1,1,3],T); # _Robert Israel_, Aug 05 2019

%o (PARI) Vecrev(digits(truncate(sqrt(-1/2+O(3^100))), 3))

%Y Cf. A271223, A309475, A309476.

%K nonn,base

%O 0,2

%A _Seiichi Manyama_, Aug 04 2019

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