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A309767
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Approximation of the 2-adic integer arctanh(4) up to 2^n.
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2
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0, 0, 0, 4, 4, 4, 4, 68, 196, 196, 708, 1732, 3780, 7876, 7876, 7876, 40644, 106180, 237252, 499396, 1023684, 1023684, 3120836, 7315140, 15703748, 15703748, 49258180, 116367044, 250584772, 250584772, 787455684, 787455684, 2934939332, 2934939332, 2934939332
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OFFSET
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0,4
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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-3)/4)} 4^(2*i+1)/(2*i+1)) mod 2^n.
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EXAMPLE
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a(3) = 4^1 mod 2^3 = 4;
a(6) = 4^1 mod 2^6 = 4
a(7) = (4^1 + 4^3/3) mod 2^7 = 68;
a(10) = (4^1 + 4^3/3) mod 2^10 = 708;
a(11) = (4^1 + 4^3/3 + 4^5/5) mod 2^11 = 1732;
a(14) = (4^1 + 4^3/3 + 4^5/5) mod 2^14 = 7876;
a(15) = (4^1 + 4^3/3 + 4^5/5 + 4^7/7) mod 2^15 = 7876.
a(18) = (4^1 + 4^3/3 + 4^5/5 + 4^7/7) mod 2^18 = 237252.
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PROG
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(PARI) a(n) = lift(sum(i=0, (n-3)/4, Mod(4^(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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STATUS
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approved
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