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%I #13 May 04 2021 09:05:00
%S 1,1,2,3,5,7,11,15,21,29,39,51,69,89,115,147,187,235,297,369,457,565,
%T 693,845,1031,1249,1507,1815,2175,2597,3099,3681,4359,5153,6073,7137,
%U 8377,9803,11447,13345,15521,18013,20881,24151,27885,32149,36999,42509,48783,55885,63931
%N The sequence e when b=[ 1,0,1,1,1,... ].
%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="/A042953/b042953.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<>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
%Y Cf. A042951, A042952.
%K nonn
%O 0,3
%A _N. J. A. Sloane_ and _J. H. Conway_
%E Terms a(42) and beyond from _Andrew Howroyd_, May 03 2021
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