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A041002 The sequence d, given that c is a left shift by one place of b. 3
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified April 17 14:32 EDT 2021. Contains 343063 sequences. (Running on oeis4.)