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A041002 The sequence d, given that c is a left shift by one place of b. 3


%S 1,3,4,7,14,18,19,20,22,23,25,26,28,29,30,31,35,36,37,38,40,41,42,45,

%T 48,49,50,52,54,55,57,59,63,67,70,71,73,79,80,83,85,87,90,91,93,94,98,

%U 100,101,102,103,106,108,110,111,112,116,117,121,124,132,135,137,142,143,144

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

%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="/A041002/b041002.txt">Table of n, a(n) for n = 0..494</a>

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

%o 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

%Y Cf. A041003, A041004.

%K nonn,easy,eigen

%O 0,2

%A _N. J. A. Sloane_

%E Terms a(28) and beyond from _Andrew Howroyd_, Apr 14 2021

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Last modified May 12 02:23 EDT 2021. Contains 343808 sequences. (Running on oeis4.)