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%I #13 Jun 22 2022 10:38:08
%S 0,0,2,2,10,26,58,122,122,122,122,1146,1146,5242,13434,29818,29818,
%T 95354,95354,95354,619642,619642,619642,4813946,4813946,21591162,
%U 21591162,21591162,21591162,290026618,290026618,290026618,2437510266,6732477562,6732477562
%N Approximation of the 2-adic integer arctanh(2) up to 2^n.
%C arctanh(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} 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 = 26;
%e a(6) = (2^1 + 2^3/3 + 2^5/5) mod 2^6 = 58;
%e a(7) = (2^1 + 2^3/3 + 2^5/5) mod 2^7 = 122.
%o (PARI) a(n) = lift(sum(i=0, n/2-1, Mod(2^(2*i+1)/(2*i+1), 2^n)))
%Y Cf. A309751, A309754.
%K nonn
%O 0,3
%A _Jianing Song_, Aug 15 2019
%E Offset corrected by _Georg Fischer_, Jun 22 2022
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