A042951 The sequence e when b=[ 0,1,1,1,1,... ].

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

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

N. J. A. Sloane and J. H. Conway

Extensions

Terms a(58) and beyond from Andrew Howroyd, May 03 2021

Status

approved