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%I #13 Jun 22 2022 10:38:18
%S 0,0,2,2,10,10,10,74,202,202,714,714,714,714,8906,25290,58058,123594,
%T 254666,516810,516810,1565386,1565386,5759690,14148298,14148298,
%U 47702730,47702730,181920458,450355914,987226826,987226826,3134710474,7429677770,7429677770
%N Approximation of the 2-adic integer arctan(2) up to 2^n.
%C arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F a(n) = (Sum_{i=0..floor(n/2)-1} (-1)^i*2^(2*i+1)/(2*i+1)) mod 2^n.
%e a(2) = 2^1 mod 2^2 = 2;
%e a(3) = 2^1 mod 2^3 = 2;
%e a(4) = (2^1 - 2^3/3) mod 2^4 = 2;
%e a(5) = (2^1 - 2^3/3) mod 2^5 = 10;
%e a(6) = (2^1 - 2^3/3 + 2^5/5) mod 2^6 = 10;
%e a(7) = (2^1 - 2^3/3 + 2^5/5) mod 2^7 = 74.
%o (PARI) a(n) = lift(sum(i=0, n/2-1, Mod((-1)^i*2^(2*i+1)/(2*i+1), 2^n)))
%Y Cf. A309752, A309753.
%K nonn
%O 0,3
%A _Jianing Song_, Aug 15 2019
%E Offset corrected by _Georg Fischer_, Jun 22 2022
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