A206482 Primes p(k) such that p(k) <= 2^(p(k+1)-p(k)) < p(k+1).

2, 3, 13, 61, 1021, 65521, 68719476731, 1427247692705959881058285969449495136382746621

Offset

1,1

Comments

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

Next gap is 900, corresponding to the 271-digit a(9). - Charles R Greathouse IV, Mar 17 2015

Links

Table of n, a(n) for n=1..8.

Example

2 is in the sequence because prime(1)=2^(prime(1+1)-prime(1))<prime(1+1) or 2=2^(3-2)<3;
3 is in the sequence because prime(2)<2^(prime(2+1)-prime(2))<prime(2+1) or 3<2^(5-3)<5;
13 is in the sequence because prime(6)<2^(prime(6+1)-prime(6))<prime(6+1) or 13<2^(17-13)<17.

Prog

(PARI) isA206482(n)={
    local(d);
    d=2^(nextprime(n+1)-n) ;
    if(isprime(n),
        if(d>=n && d< nextprime(n+1),
            return(1),
            return(0)
        ),
     return(0)
    )
}
{
for(po=1, 200,
    n =precprime(2^po) ;
    if (isA206482(n) , print(n)) ;
) ;
} \\ R. J. Mathar, Feb 22 2012

Crossrefs

Cf. A000040, A001223.

Sequence in context: A184179 A100102 A208202 * A164582 A068945 A219698

Adjacent sequences: A206479 A206480 A206481 * A206483 A206484 A206485

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 15 2012

Status

approved