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Beginning with a(1)=2, a(n+1) is the a(n)-th palindromic prime.
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%I #8 Dec 11 2012 19:39:11

%S 2,3,5,11,313,3075703,946287424782649

%N Beginning with a(1)=2, a(n+1) is the a(n)-th palindromic prime.

%C Assuming that no phenomenally strong sieve or counting algorithm for palindromic primes is discovered, a(8) (which is in the vicinity of 10^35) will be beyond reach for at least several years even with the best computing environment.

%F A220346(n+1) = A002385(A220346(n)).

%t palQ[n_] := Module[{d = IntegerDigits[n]}, d == Reverse[d]]; t = {2}; p = 0; cnt = 0; Table[While[cnt < t[[-1]], While[p = NextPrime[p]; ! palQ[p]]; cnt++]; AppendTo[t, p], {5}]; t (* _T. D. Noe_, Dec 11 2012 *)

%Y Cf. A002385.

%K nonn,base,hard

%O 1,1

%A _James G. Merickel_, Dec 11 2012