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A259744 Smallest prime p such that, for every positive integer k <= n, the concatenation of p, prime(k)^2 and reverse(p) is prime.

%I A259744 #16 Aug 16 2015 18:04:02
%S A259744 11,17,1097,7949,780587,123638027,3259714649,76526081651
%N A259744 Smallest prime p such that, for every positive integer k <= n, the concatenation of p, prime(k)^2 and reverse(p) is prime.
%C A259744 a(8) found by _Hans Havermann_.
%H A259744 Carlos Rivera Puzzles, <a href="http://www.primepuzzles.net/puzzles/puzz_788.htm">Puzzle 788. P&p(i)^2&RP</a>
%e A259744 a(3)=1097 because 109747901 (1097&2^2&7901) and 109797901 (1097&3^2&7901) and 1097257901 (1097&5^2&7901) are prime numbers, and 1097 is the smallest prime for which this is the case.
%t A259744 f[n_, k_] := FromDigits[Join[
%t A259744    IntegerDigits[n], IntegerDigits[Prime[k]^2],
%t A259744    Reverse[IntegerDigits[n]]]]
%t A259744 a[n_] := Module[{p = 2, k = 1},
%t A259744   While[k <= n,
%t A259744    If[PrimeQ[f[p, k]], k++, p = NextPrime[p]; k = 1];
%t A259744    ];
%t A259744   Return[p]
%t A259744 ](* _Kellen Myers_, Aug 16 2015 , note this is very slow *)
%K A259744 nonn,base,more
%O A259744 1,1
%A A259744 _Vicente Izquierdo Gomez_, Jul 04 2015