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A321081 Digits of the 2-adic integer log_5(-3).

%I A321081 #12 Nov 21 2018 07:31:04
%S A321081 1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,1,0,1,0,0,1,
%T A321081 1,0,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,1,0,1,1,0,1,1,1,1,1,0,0,1,1,0,1,0,
%U A321081 0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,1
%N A321081 Digits of the 2-adic integer log_5(-3).
%C A321081 See A321080 for the definition of log_5(-3) and more information.
%C A321081 Multiplicative inverse of A321083.
%H A321081 Jianing Song, <a href="/A321081/b321081.txt">Table of n, a(n) for n = 0..1000</a>
%H A321081 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A321081 a(n) = 0 if 5^A321080(n+2) + 3 is divisible by 2^(n+3), otherwise 1.
%F A321081 Equals to A321694/A152228.
%e A321081 log_5(-3) = ...1000011001011001010001001010011010100011.
%o A321081 (PARI) b(n) = {my(v=vector(n)); v[2]=0; for(n=3, n, v[n] = v[n-1] + if(Mod(5,2^n)^v[n-1] + 3==0, 0, 2^(n-3))); v}
%o A321081 a(n) = b(n+3)[n+3]\2^n
%Y A321081 Cf. A321080, A321083, A321694.
%K A321081 nonn,base
%O A321081 0,1
%A A321081 _Jianing Song_, Oct 27 2018