A287117 Numbers with no odd prime binary proper prefixes.

1, 2, 3, 4, 5, 8, 9, 16, 17, 18, 19, 32, 33, 36, 37, 64, 65, 66, 67, 72, 73, 128, 129, 130, 131, 132, 133, 144, 145, 256, 257, 258, 259, 260, 261, 264, 265, 266, 267, 288, 289, 290, 291, 512, 513, 516, 517, 518, 519, 520, 521, 522, 523, 528, 529, 530, 531, 532, 533, 534, 535

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Dan Brumleve, Does the sum of reciprocals of all prime-prefix-free numbers converge?, Math StackExchange, May 20 2017.

Example

131, while prime itself, has proper binary prefixes 65, 32, 16, 8, 4, 2, 1, none of which are odd primes.

Mathematica

Select[Range@535, AllTrue[ Floor[#/2 ^ Range@Log2@#], ! (# > 2 && PrimeQ[#]) &] &] (* Giovanni Resta, May 20 2017 *)

Prog

(Perl)
sub isp {
  my $x = shift;
  for my $d (2 .. $x - 1) {
    return 0 if $x % $d == 0;
  }
  return 1;
}
sub rots {
  my $x = shift;
  my @x;
  while ($x > 5) {
    $x = int($x / 2);
    push @x, $x;
  }
  @x
}
for my $i (1 .. $ARGV[0] // 200) {
  my @np = grep isp($_), rots($i);
  push @z, $i if @np == 0;
}
print join(", ", @z) . "\n";

Crossrefs

Sequence in context: A085152 A264886 A369294 * A286431 A015931 A330400

Adjacent sequences: A287114 A287115 A287116 * A287118 A287119 A287120

Keyword

nonn,easy,base

Author

Dan Brumleve, May 20 2017

Status

approved