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 A287117 Numbers with no odd prime binary proper prefixes. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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: A301464 A085152 A264886 * A286431 A015931 A330400 Adjacent sequences:  A287114 A287115 A287116 * A287118 A287119 A287120 KEYWORD nonn,easy,base AUTHOR Dan Brumleve, May 20 2017 STATUS approved

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)