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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For n > 10, a(n) == -1 (mod 2*3*5*11*13). - Farideh Firoozbakht, Apr 24 2004 LINKS C. K. Caldwell, Latest results about Cunningham Chains 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

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Last modified June 7 01:26 EDT 2020. Contains 334836 sequences. (Running on oeis4.)