this is because multiples of 3 and 5 coincides with oeis serie A001969 just until 17 which is a prime number (as many in the serie) so cannot be multiple of 3 nor 5 (but i learned about binary weight..).

pardon me, was late and i was searching some oneliner to write while waiting sleep coming upon me..

what follow is original post:

not so elegantly, but here my oneliner solution:

perl -e "print eval join '+',grep{((scalar @{[((sprintf '%b',$_)=~/1/g
+)]}))%2==0} 0..$ARGV[0];" 10

33
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perl -e "print eval join '+',grep{(0.5*(4*$_+1-(-1)**scalar @{[((sprin
+tf '%b',$_)=~/1/g)]}))%2==0} 0..$ARGV[0];" 10

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The solution is based based on the fact that 0, 3, 5, 6, 9, 10, 12,.. is also the oeis serie A001969.

Here my first attempt

use strict;
use warnings;


my $max = $ARGV[0]||10;
my $total;
my $num=0;
while ( evil_numbers($num)<= $max) {$total += evil_numbers($num);$num+
++}
print "$max gives a total of $total\n\n";

sub evil_numbers{                # https://oeis.org/A001969
      my $n = shift;             # nasty binary weight: https://oeis.o
+rg/A000120
      return 0.5 * (4 * $n + 1 - (-1) **scalar @{[((sprintf '%b',$n)=~
+/1/g)]}  );

}
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L*