A042951 - OEIS

%I #16 May 04 2021 01:13:29

%S 1,0,1,1,1,1,3,1,3,3,3,3,7,3,7,7,7,7,13,7,13,13,13,13,23,13,23,23,23,

%T 23,37,23,37,37,37,37,57,37,57,57,57,57,83,57,83,83,83,83,119,83,119,

%U 119,119,119,165,119,165,165,165,165,225,165,225,225,225,225

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

%C 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.

%C This produces 2 new sequences: d={i:c_i=1} and e=[ 1,e_1,... ] where C=1+Sum e_i*x^i.

%H Andrew Howroyd, <a href="/A042951/b042951.txt">Table of n, a(n) for n = 0..1000</a>

%o (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

%o seq(n)={my(u=vector(n, i, i>1), 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

%Y Cf. A041003, A042953, A042955, A042957, A042959, A042961.

%K nonn

%O 0,7

%A _N. J. A. Sloane_ and _J. H. Conway_

%E Terms a(58) and beyond from _Andrew Howroyd_, May 03 2021