A209611 Primes p(n) such that p(n)*(p(n+1)-p(n)) <= 2^(p(n+1)-p(n)).

2, 113, 199, 211, 293, 317, 523, 773, 839, 863, 887, 953, 1069, 1129, 1259, 1327, 1381, 1637, 1669, 1759, 1831, 1913, 1933, 1951, 2113, 2161, 2179, 2221, 2251, 2311, 2477, 2503, 2557, 2593, 2803, 2861, 2971, 3089, 3121, 3137, 3229, 3271, 3373, 3391, 3413, 3433

Offset

1,1

Comments

Primes prime(n) which multiplied by the associated prime gap g=A001223(n) remain <= 2^g.

Links

Table of n, a(n) for n=1..46.

Example

2 is in the sequence because 2*(3-2) = 2^(3-2), 113 is in the sequence because 113*(127-113) < 2^(127-113).

Prog

(PARI) isA209611(p)={
   local(q=nextprime(p+1)-p) ;
   return(isprime(p) && p*q <= 2^q) ; }
{
forprime(p=2, 3100, if(isA209611(p), print1(p" ") ) ; ) ;
} /* R. J. Mathar, Mar 19 2012 */

Crossrefs

Sequence in context: A165975 A051590 A091302 * A042567 A142112 A285145

Adjacent sequences: A209608 A209609 A209610 * A209612 A209613 A209614

Keyword

nonn

Author

Gerasimov Sergey, Mar 10 2012

Status

approved