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.

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

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 A378836 A192357

Adjacent sequences: A185541 A185542 A185543 * A185545 A185546 A185547

Keyword

nonn

Author

N. J. A. Sloane, Feb 05 2011

Status

approved