|
%I #13 Feb 04 2020 06:35:00
%S 2,5,7,7,79,79,345431,21171649,34640153,4174239239,268130051191,
%T 268130051191,253134809926049,253134809926049,253134809926049
%N Initial prime of a prime chain of length n under the iteration x->5x+6.
%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="https://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) = 13 since 7, f(7) = 41, and f(41) = 211 are primes when f(x) = 5*x + 6.
%t c[p_] := Block[{k=1, q = 5*p+6}, While[PrimeQ[q], q = 5*q+6; 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, A084956, A084957, A084958, A084960, A084961.
%K nonn,more
%O 1,1
%A _W. Edwin Clark_, Jun 14 2003
%E a(7) corrected and a(8)-a(10) from _Donovan Johnson_, Sep 27 2008
%E a(11)-a(12) from _John Cerkan_, Jan 11 2017
%E a(13)-a(15) from _Giovanni Resta_, Mar 22 2017
|
