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%I #15 Mar 23 2017 10:06:31
%S 2,3,3,23,3203,34613,165443,1274803,26314573,26314573,590256673403,
%T 15113026057043,334156170011893,3998669569752373
%N Initial prime of the first prime chain of length n under the iteration x -> 3x+4.
%C This is a special case of prime chains generated by f(x) = cx + d.
%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) = 3 since 3, f(3) = 13 and f(13) = 43 are primes when f(x) = 3*x + 4.
%t c[p_] := Block[{k=1, q=3*p + 4}, While[PrimeQ[q], q=3*q+4; k++]; k]; a[n_] := Block[{p = 2}, While[c[p] < n, p = NextPrime[p]]; p]; Array[a, 7] (* _Giovanni Resta_, Mar 22 2017 *)
%Y Cf. A057330, A057331, A083388, A084954, A084955, A084957, A084958, A084959, A084960, A084961.
%K more,nonn
%O 1,1
%A _W. Edwin Clark_, Jun 14 2003
%E a(9)-a(10) from _Donovan Johnson_, Sep 27 2008
%E a(11)-a(12) from _John Cerkan_, Jan 13 2017
%E a(13)-a(14) from _Giovanni Resta_, Mar 22 2017