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A042959 The sequence e when b=[ 1,1,1,1,0,1,1,1,... ]. 2


%S 1,1,1,1,1,2,3,3,3,3,5,7,9,9,9,11,15,19,21,21,25,31,39,45,49,53,63,75,

%T 87,97,107,121,143,165,187,207,233,265,303,341,381,425,479,541,611,

%U 681,761,849,951,1063,1185,1315,1465,1631,1817,2019,2241,2483,2755,3051,3379

%N The sequence e when b=[ 1,1,1,1,0,1,1,1,... ].

%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="/A042959/b042959.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<>5), 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, A042958.

%K nonn

%O 0,6

%A _N. J. A. Sloane_ and _J. H. Conway_

%E Terms a(52) and beyond from _Andrew Howroyd_, May 03 2021

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Last modified July 27 05:26 EDT 2021. Contains 346305 sequences. (Running on oeis4.)