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A309753
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Approximation of the 2-adic integer arctanh(2) up to 2^n.
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4
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0, 0, 2, 2, 10, 26, 58, 122, 122, 122, 122, 1146, 1146, 5242, 13434, 29818, 29818, 95354, 95354, 95354, 619642, 619642, 619642, 4813946, 4813946, 21591162, 21591162, 21591162, 21591162, 290026618, 290026618, 290026618, 2437510266, 6732477562, 6732477562
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OFFSET
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0,3
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COMMENTS
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arctanh(x) = x + x^3/3 + x^5/5 + x^7/7 + ...
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LINKS
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FORMULA
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a(n) = (Sum_{i=0..floor(n/2)-1} 2^(2*i+1)/(2*i+1)) mod 2^n.
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EXAMPLE
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a(2) = 2^1 mod 2^2 = 2;
a(3) = 2^1 mod 2^3 = 2;
a(4) = (2^1 + 2^3/3) mod 2^4 = 2;
a(5) = (2^1 + 2^3/3) mod 2^5 = 26;
a(6) = (2^1 + 2^3/3 + 2^5/5) mod 2^6 = 58;
a(7) = (2^1 + 2^3/3 + 2^5/5) mod 2^7 = 122.
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PROG
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(PARI) a(n) = lift(sum(i=0, n/2-1, Mod(2^(2*i+1)/(2*i+1), 2^n)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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