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A206482 Primes p(k) such that p(k) <= 2^(p(k+1)-p(k)) < p(k+1). 1
2, 3, 13, 61, 1021, 65521, 68719476731, 1427247692705959881058285969449495136382746621 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 02:48 EDT 2021. Contains 347605 sequences. (Running on oeis4.)