A042957 The sequence e when b=[ 1,1,1,0,1,1,... ].

1, 1, 1, 1, 2, 3, 3, 3, 5, 7, 9, 9, 11, 15, 19, 21, 25, 31, 39, 45, 53, 63, 75, 87, 103, 121, 143, 165, 193, 225, 263, 301, 347, 401, 467, 535, 613, 701, 807, 921, 1053, 1197, 1365, 1551, 1767, 2003, 2269, 2563, 2905, 3281, 3705, 4167, 4697, 5285, 5947, 6669

Offset

0,5

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<>4), 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, A042956.

Sequence in context: A036029 A181530 A035362 * A341074 A343885 A264870

Adjacent sequences: A042954 A042955 A042956 * A042958 A042959 A042960

Keyword

nonn

Author

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

Extensions

Terms a(48) and beyond from Andrew Howroyd, May 03 2021

Status

approved