%I #13 May 04 2021 09:05:20
%S 1,1,1,1,2,3,3,3,5,7,9,9,11,15,19,21,25,31,39,45,53,63,75,87,103,121,
%T 143,165,193,225,263,301,347,401,467,535,613,701,807,921,1053,1197,
%U 1365,1551,1767,2003,2269,2563,2905,3281,3705,4167,4697,5285,5947,6669
%N The sequence e when b=[ 1,1,1,0,1,1,... ].
%C 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.
%C This produces 2 new sequences: d={i:c_i=1} and e=[ 1,e_1,... ] where C=1+Sum e_i*x^i.
%H Andrew Howroyd, <a href="/A042957/b042957.txt">Table of n, a(n) for n = 0..1000</a>
%o (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
%o seq(n)={my(u=vector(n, i, i<>4), 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
%Y Cf. A042951, A042956.
%K nonn
%O 0,5
%A _N. J. A. Sloane_ and _J. H. Conway_
%E Terms a(48) and beyond from _Andrew Howroyd_, May 03 2021
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