A042953 The sequence e when b=[ 1,0,1,1,1,... ].

1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 39, 51, 69, 89, 115, 147, 187, 235, 297, 369, 457, 565, 693, 845, 1031, 1249, 1507, 1815, 2175, 2597, 3099, 3681, 4359, 5153, 6073, 7137, 8377, 9803, 11447, 13345, 15521, 18013, 20881, 24151, 27885, 32149, 36999, 42509, 48783, 55885, 63931

Offset

0,3

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<>2), 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, A042952.

Sequence in context: A035969 A355027 A332745 * A023028 A246579 A232480

Adjacent sequences: A042950 A042951 A042952 * A042954 A042955 A042956

Keyword

nonn

Author

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

Extensions

Terms a(42) and beyond from Andrew Howroyd, May 03 2021

Status

approved