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A042953
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The sequence e when b=[ 1,0,1,1,1,... ].
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3
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1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 39, 51, 69, 89, 115, 147, 187, 235, 297, 369, 457, 565, 693, 845, 1031, 1249, 1507, 1815, 2175, 2597, 3099, 3681, 4359, 5153, 6073, 7137, 8377, 9803, 11447, 13345, 15521, 18013, 20881, 24151, 27885, 32149, 36999, 42509, 48783, 55885, 63931
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OFFSET
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0,3
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COMMENTS
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Map a binary sequence b=[ b_1,... ] to a binary sequence c=[ c_1,... ] so that C=1/Product (1-x^i)^c_i == 1+Sum b_i*x^i mod 2.
This produces 2 new sequences: d={i:c_i=1} and e=[ 1,e_1,... ] where C=1+Sum e_i*x^i.
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LINKS
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PROG
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(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(u=vector(n, i, i<>2), v=vector(n)); for(n=1, #v, v[n]=(u[n] + EulerT(v[1..n])[n])%2); concat([1], EulerT(v))} \\ Andrew Howroyd, May 03 2021
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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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