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%I #22 Feb 04 2019 09:44:09
%S 2,3,5,29,1129,10009,575119,32694619,586130089,1030544269,
%T 427744892959,18736892249459,221530676461709,221530676461709
%N a(n) = beginning of a run of at least n primes when x -> 3*x + 2 is iterated.
%C a(11) > 8695354111. - _Donovan Johnson_, Sep 27 2008
%H D. H. Lehmer, <a href="http://dx.doi.org/10.1112/plms/s3-14A.1.183">On certain chains of primes</a>, Proc. London Math. Soc. (3) 14a 1965 183-186.
%e a(3) = 5 because 5 is the beginning of 3 primes in succession: 5, 3*5 + 2 = 17 is prime and 3*17 + 2 = 53 is prime.
%t c[p_] := Block[{k=1, q = 3 p + 2}, While[PrimeQ[q], q = 3 q + 2; k++]; k]; a[n_] := Block[{p=2}, While[c[p] < n, p = NextPrime[p]]; p]; Array[a, 7] (* _Giovanni Resta_, Mar 21 2017 *)
%o (PARI) mx=1; forprime(p=1,198000,x=p; m=0; while(isprime(x=3*x+2),m=m+1; if(m>mx,print(p," ",m, " ",x); mx=m,))) \\ _Donald S. McDonald_, Jun 11 2003
%Y Cf. A057331, A081173.
%K nonn
%O 1,1
%A _W. Edwin Clark_, Jun 09 2003
%E a(8)-a(10) from _Donovan Johnson_, Sep 27 2008
%E a(11)-a(12) from _John Cerkan_, Jan 09 2017
%E a(13)-a(14) from _Giovanni Resta_, Mar 21 2017
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