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 A042951 The sequence e when b=[ 0,1,1,1,1,... ]. 7
 1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 3, 3, 7, 3, 7, 7, 7, 7, 13, 7, 13, 13, 13, 13, 23, 13, 23, 23, 23, 23, 37, 23, 37, 37, 37, 37, 57, 37, 57, 57, 57, 57, 83, 57, 83, 83, 83, 83, 119, 83, 119, 119, 119, 119, 165, 119, 165, 165, 165, 165, 225, 165, 225, 225, 225, 225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS 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. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} seq(n)={my(u=vector(n, i, i>1), 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 CROSSREFS Cf. A041003, A042953, A042955, A042957, A042959, A042961. Sequence in context: A025796 A024163 A029155 * A194299 A029154 A211974 Adjacent sequences:  A042948 A042949 A042950 * A042952 A042953 A042954 KEYWORD nonn AUTHOR EXTENSIONS Terms a(58) and beyond from Andrew Howroyd, May 03 2021 STATUS approved

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Last modified July 23 14:33 EDT 2021. Contains 346259 sequences. (Running on oeis4.)