A042952 The sequence d when b=[ 1,0,1,1,1,... ].

1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 17, 18, 19, 21, 25, 27, 30, 31, 32, 35, 38, 41, 42, 47, 50, 54, 59, 61, 62, 63, 68, 73, 76, 78, 80, 81, 83, 84, 89, 90, 91, 94, 96, 97, 101, 102, 103, 104, 108, 112, 114, 118, 119, 120, 125, 126, 128, 130, 131, 133, 139, 144, 150, 157, 160

Offset

0,2

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..302

Prog

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
upto(n)={my(u=vector(n, i, i<>2), v=vector(n)); for(n=1, #v, v[n]=(u[n] + EulerT(v[1..n])[n])%2); select(t->t, v, 1)} \\ Andrew Howroyd, May 03 2021

Crossrefs

Cf. A042953, A042954, A042956, A042958.

Sequence in context: A245761 A371248 A059759 * A126327 A328116 A193286

Adjacent sequences: A042949 A042950 A042951 * A042953 A042954 A042955

Keyword

nonn

Author

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

Extensions

Terms a(35) and beyond from Andrew Howroyd, May 03 2021

Status

approved