A079793 Smallest multiple of n having an equal number of ones and zeros and no other digits.

10, 10, 100011, 1100, 10, 100110, 1001, 111000, 100000000011111111, 10, 1001, 101100, 1001, 101010, 100110, 11110000, 100011, 100000000111111110, 110010, 1100, 101010, 1100, 11010100, 111000, 1100, 101010

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..890

Maple

F:= proc(m)
     uses Optimization;
     local dmax, dmin, dmax0, cons, obj, i, j, x, r, R;
     dmin:= max(padic:-ordp(m, 2), padic:-ordp(m, 5));
     dmax0:= max(1, 2*dmin-1);
     if dmax0::even then dmax0:= dmax0+1 fi;
     for dmax from dmax0 to 38 by 2 do
        x:= 'x':
        x[dmax]:= 1:
        cons:= [add((10^i mod m) * x[i], i=dmin..dmax) = r * m,
                           add(x[i], i=dmin..dmax) = (1+dmax)/2,
                           seq(seq(`if`(10^i mod m = 10^j mod m, x[i] >= x[j], NULL), i=dmin..j-1), j=dmin+1..dmax-1)                   ];
        obj:= add(10^i * x[i], i=dmin..dmax-1);
        if dmax = dmin then
          if dmax = 1 and (10 mod m = 0) then return 10 else next fi fi;
        R:= traperror(Minimize(obj, cons, assume=nonnegint, binaryvariables = [seq(x[i], i=dmin..dmax-1)], depthlimit=100));
        if R = "no feasible integer point found; use feasibilitytolerance option to adjust tolerance" then next
        elif R = lasterror then printf("%s for dmax=%d at m=%d\n", R, dmax, m)
        else return (R[1]+10^dmax) fi
     od;
     FAIL
end proc:
map(F, [$1..100]); # Robert Israel, Dec 04 2024

Crossrefs

Sequence in context: A364773 A052983 A072804 * A086884 A284201 A324660

Adjacent sequences: A079790 A079791 A079792 * A079794 A079795 A079796

Keyword

base,nonn

Author

Amarnath Murthy, Mar 27 2004

Extensions

Corrected and extended by Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 12 2004

Name clarified by Robert Israel, Dec 03 2024

Status

approved