A041002 The sequence d, given that c is a left shift by one place of b.

1, 3, 4, 7, 14, 18, 19, 20, 22, 23, 25, 26, 28, 29, 30, 31, 35, 36, 37, 38, 40, 41, 42, 45, 48, 49, 50, 52, 54, 55, 57, 59, 63, 67, 70, 71, 73, 79, 80, 83, 85, 87, 90, 91, 93, 94, 98, 100, 101, 102, 103, 106, 108, 110, 111, 112, 116, 117, 121, 124, 132, 135, 137, 142, 143, 144

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..494

Prog

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
upto(n)={my(v=vector(n+1)); v[1]=1; for(n=2, #v, v[n]=(v[n-1]+EulerT(v[2..n])[n-1])%2); select(t->t, v[2..n+1], 1)} \\ Andrew Howroyd, Apr 14 2021

Crossrefs

Cf. A041003, A041004.

Sequence in context: A254310 A121174 A050071 * A062203 A319548 A095063

Adjacent sequences: A040999 A041000 A041001 * A041003 A041004 A041005

Keyword

nonn,easy,eigen

Author

N. J. A. Sloane

Extensions

Terms a(28) and beyond from Andrew Howroyd, Apr 14 2021

Status

approved