A042955 The sequence e when b=[ 1,1,0,1,1,... ].

1, 1, 1, 2, 3, 3, 5, 7, 9, 11, 15, 19, 25, 31, 39, 49, 61, 73, 91, 111, 135, 163, 197, 235, 283, 335, 399, 473, 559, 655, 773, 903, 1057, 1233, 1435, 1663, 1933, 2231, 2575, 2969, 3419, 3921, 4501, 5151, 5891, 6723, 7665, 8723, 9925, 11261, 12773

Offset

0,4

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<>3), 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. A042951, A042954.

Sequence in context: A030729 A111865 A238873 * A035553 A108961 A017984

Adjacent sequences: A042952 A042953 A042954 * A042956 A042957 A042958

Keyword

nonn

Author

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

Extensions

Terms a(45) and beyond from Andrew Howroyd, May 03 2021

Status

approved