cp's OEIS Frontend

A309753 Approximation of the 2-adic integer arctanh(2) up to 2^n.

%I A309753 #13 Jun 22 2022 10:38:08
%S A309753 0,0,2,2,10,26,58,122,122,122,122,1146,1146,5242,13434,29818,29818,
%T A309753 95354,95354,95354,619642,619642,619642,4813946,4813946,21591162,
%U A309753 21591162,21591162,21591162,290026618,290026618,290026618,2437510266,6732477562,6732477562
%N A309753 Approximation of the 2-adic integer arctanh(2) up to 2^n.
%C A309753 arctanh(x) = x + x^3/3 + x^5/5 + x^7/7 + ...
%H A309753 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A309753 a(n) = (Sum_{i=0..floor(n/2)-1} 2^(2*i+1)/(2*i+1)) mod 2^n.
%e A309753 a(2) = 2^1 mod 2^2 = 2;
%e A309753 a(3) = 2^1 mod 2^3 = 2;
%e A309753 a(4) = (2^1 + 2^3/3) mod 2^4 = 2;
%e A309753 a(5) = (2^1 + 2^3/3) mod 2^5 = 26;
%e A309753 a(6) = (2^1 + 2^3/3 + 2^5/5) mod 2^6 = 58;
%e A309753 a(7) = (2^1 + 2^3/3 + 2^5/5) mod 2^7 = 122.
%o A309753 (PARI) a(n) = lift(sum(i=0, n/2-1, Mod(2^(2*i+1)/(2*i+1), 2^n)))
%Y A309753 Cf. A309751, A309754.
%K A309753 nonn
%O A309753 0,3
%A A309753 _Jianing Song_, Aug 15 2019
%E A309753 Offset corrected by _Georg Fischer_, Jun 22 2022