A042962 The sequence e when b=[ 1,0,1,0,1,0,1,0,... ].

1, 1, 2, 3, 4, 5, 8, 9, 12, 15, 18, 21, 28, 31, 38, 45, 52, 59, 72, 79, 92, 105, 118, 131, 154, 167, 190, 213, 236, 259, 296, 319, 356, 393, 430, 467, 524, 561, 618, 675, 732, 789, 872, 929, 1012, 1095, 1178, 1261, 1380, 1463, 1582, 1701, 1820, 1939, 2104, 2223

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 04 2021

Crossrefs

Cf. A042951.

Sequence in context: A109850 A008749 A029000 * A027584 A161240 A165652

Adjacent sequences: A042959 A042960 A042961 * A042963 A042964 A042965

Keyword

nonn

Author

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

Extensions

Terms a(48) and beyond from Andrew Howroyd, May 04 2021

Status

approved