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 A287638 Odd primes with no other odd primes as prefixes in binary. 1
 3, 5, 17, 19, 37, 67, 73, 131, 257, 521, 523, 577, 1033, 1039, 1061, 1063, 1069, 1153, 1163, 2053, 2069, 2081, 2083, 2089, 2113, 2129, 2131, 2137, 2141, 2143, 2333, 4099, 4111, 4129, 4153, 4177, 4229, 4231, 4241, 4243, 4261, 4271, 4273, 4637, 4639, 4643, 4649, 4651, 4657, 4663 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sum of the reciprocals converges by the Kraft-McMillan inequality. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Dan Brumleve, Does the sum of reciprocals of all prime-prefix-free numbers converge?, Math StackExchange, May 20 2017. Wikipedia, Kraft-McMillan inequality EXAMPLE 4663 is an odd prime with proper binary prefixes 2331, 1165, 582, 291, 145, 72, 36, 18, 9, 4, 2, 1, and none of these are odd primes. PROG (perl) sub isp {   my \$x = shift;   return 0 if \$x < 2;   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] // 8000) {   my @np = grep isp(\$_), rots(\$i);   push @z, \$i if isp(\$i) && \$i % 2 && @np == 0; } print join(", ", @z) . "\n"; (PARI) is(n)=if(!isprime(n) || n<3, return(0)); while(n>3, if(isprime(n>>=1), return(n==2))); 1 \\ Charles R Greathouse IV, Jun 12 2017 CROSSREFS Odd prime elements of A287117. Sequence in context: A045415 A045416 A038891 * A119768 A020592 A295387 Adjacent sequences:  A287635 A287636 A287637 * A287639 A287640 A287641 KEYWORD nonn,easy,base AUTHOR Dan Brumleve, May 28 2017 STATUS approved

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Last modified August 7 09:09 EDT 2020. Contains 336274 sequences. (Running on oeis4.)