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A185544 Convert n to binary, use as coefficients of polynomial in GF(2)[x], apply the map f defined in A185000, write down coefficient vector of the result, highest powers first. 4
0, 10, 1, 111, 10, 1000, 11, 1101, 100, 10110, 101, 10011, 110, 11100, 111, 11001, 1000, 101010, 1001, 101111, 1010, 100000, 1011, 100101, 1100, 111110, 1101, 111011, 1110, 110100, 1111, 110001, 10000, 1010010, 10001, 1010111, 10010, 1011000, 10011, 1011101, 10100, 1000110, 10101, 1000011, 10110, 1001100, 10111, 1001001, 11000, 1111010, 11001, 1111111, 11010, 1110000, 11011, 1110101, 11100, 1101110, 11101, 1101011, 11110, 1100100, 11111 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

EXAMPLE

n=3, polynomial is x+1, f(x+1) = x^2+x+1, so a(3) = 111.

n=4, polynomial is x^2, f(x^2) = x, so a(4) = 10.

MAPLE

# Extract coefficient vector polynomial (decreasing powers):

coeflistD:=proc(f) local d, i, t1, t2, t3, t4;

if f=0 then RETURN([0]); else

d:=degree(f);

t1:=subs(x=1/x, f);

t2:=sort(expand(x^d*t1));

t3:=seriestolist(series(t2, x, d+2));

t4:=nops(t3);

if t4<d+1 then for i from t4+1 to d+1 do t3:=[op(t3), 0]; od: fi;

RETURN(t3);

fi;

end;

# Define map f:

f:=a->if subs(x=0, a) = 0 then expand(simplify(a/x)) mod 2;

else t1:=((x^2+1)*a+1)/x; expand(t1) mod 2; fi;

for n from 0 to 10000 do

t1:=convert(n, base, 2);

t2:=add(t1[i]*x^(i-1), i=1..nops(t1));

t3:=f(t2);

t4:=coeflistD(t3);

lprint(t4);

od:

CROSSREFS

Sequence in context: A181868 A287494 A287753 * A048882 A192357 A156286

Adjacent sequences:  A185541 A185542 A185543 * A185545 A185546 A185547

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 05 2011

STATUS

approved

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Last modified January 26 06:41 EST 2022. Contains 350572 sequences. (Running on oeis4.)