A042952 - OEIS

%I #13 May 04 2021 09:04:52

%S 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,

%T 54,59,61,62,63,68,73,76,78,80,81,83,84,89,90,91,94,96,97,101,102,103,

%U 104,108,112,114,118,119,120,125,126,128,130,131,133,139,144,150,157,160

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

%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="/A042952/b042952.txt">Table of n, a(n) for n = 0..302</a>

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

%o 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

%Y Cf. A042953, A042954, A042956, A042958.

%K nonn

%O 0,2

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

%E Terms a(35) and beyond from _Andrew Howroyd_, May 03 2021