A206482 - OEIS

%I #22 Mar 17 2015 13:27:11

%S 2,3,13,61,1021,65521,68719476731,

%T 1427247692705959881058285969449495136382746621

%N Primes p(k) such that p(k) <= 2^(p(k+1)-p(k)) < p(k+1).

%C The associated prime gaps p(k+1)-p(k) are 1, 2, 4, 6, 10, 16, 36, 150,..

%C Next gap is 900, corresponding to the 271-digit a(9). - _Charles R Greathouse IV_, Mar 17 2015

%e 2 is in the sequence because prime(1)=2^(prime(1+1)-prime(1))<prime(1+1) or 2=2^(3-2)<3;

%e 3 is in the sequence because prime(2)<2^(prime(2+1)-prime(2))<prime(2+1) or 3<2^(5-3)<5;

%e 13 is in the sequence because prime(6)<2^(prime(6+1)-prime(6))<prime(6+1) or 13<2^(17-13)<17.

%o (PARI) isA206482(n)={

%o     local(d);

%o     d=2^(nextprime(n+1)-n) ;

%o     if(isprime(n),

%o         if(d>=n && d< nextprime(n+1),

%o             return(1),

%o             return(0)

%o         ),

%o      return(0)

%o     )

%o }

%o {

%o for(po=1,200,

%o     n =precprime(2^po) ;

%o     if (isA206482(n) , print(n)) ;

%o ) ;

%o } \\ R. J. Mathar, Feb 22 2012

%Y Cf. A000040, A001223.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Feb 15 2012