

A057331


a(n) = smallest prime p such that the first n iterates of p under x>2x+1 are all primes.


20



2, 2, 2, 2, 2, 89, 1122659, 19099919, 85864769, 26089808579, 554688278429, 554688278429, 4090932431513069, 95405042230542329
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OFFSET

0,1


COMMENTS

For n > 10, a(n) == 1 (mod 2*3*5*11*13).  Farideh Firoozbakht, Apr 24 2004


LINKS

Table of n, a(n) for n=0..13.
C. K. Caldwell, Latest results about Cunningham Chains
Index entries for sequences related to primes in arithmetic progressions


EXAMPLE

a(5) = 89 because the numbers 89, 179, 359, 719, 1439, 2879 are all primes and 89 is the first number to have this property.


MATHEMATICA

f[n_] := 2n + 1; k = 1; Do[ While[ Union[ PrimeQ[ NestList[ f, Prime[k], n]]] != {True}, k++ ]; Print[ Prime[k]], {n, 1, 9} ]


PROG

(PARI) has(p, n)=for(k=1, n, if(!isprime(p), return(0)); p=2*p+1); isprime(p)
a(n)=forprime(p=2, , if(has(p, n), return(p))) \\ Charles R Greathouse IV, Apr 29 2015


CROSSREFS

See also A005602.
Sequence in context: A029665 A256223 A056993 * A270374 A067089 A090872
Adjacent sequences: A057328 A057329 A057330 * A057332 A057333 A057334


KEYWORD

nonn,nice,more


AUTHOR

Patrick De Geest, Aug 15 2000


EXTENSIONS

More terms from Farideh Firoozbakht, Apr 24 2004
a(11) (from the Caldwell link) sent by Peter Deleu, Hulste, Belgium, Nov 22 2004
a(13) added from A005602, Paul Zimmermann, Mar 09 2018


STATUS

approved



