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

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, 87, 97, 107, 121, 143, 165, 187, 207, 233, 265, 303, 341, 381, 425, 479, 541, 611, 681, 761, 849, 951, 1063, 1185, 1315, 1465, 1631, 1817, 2019, 2241, 2483, 2755, 3051, 3379

Offset

0,6

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<>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

Crossrefs

Cf. A042951, A042958.

Sequence in context: A253591 A129263 A035367 * A147815 A227246 A200924

Adjacent sequences: A042956 A042957 A042958 * A042960 A042961 A042962

Keyword

nonn

Author

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

Extensions

Terms a(52) and beyond from Andrew Howroyd, May 03 2021

Status

approved