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%I #1 Jun 01 2010 03:00:00
%S 3,3,1,11,1,1,1,1,1,1,3,7,31,13,9,1,1,141,53,37,9,11,1,7,61,7,17,13,
%T 17,1,17,11,7,23,7,27,27,7,1,9,19,29,7,29,19,3,3,1,43,67,1,7,7,9,9,1,
%U 13,21,7,7,7,1,1,43,1,1,57,1,67,7,17
%N Smallest natural square base q = q(k) that concatenation prime(k)//prime(k+1)//q^2 (k = 1, 2, ...) is a prime number.
%C Note two consecutive primes prime(k)//prime(k+1)
%C Necessarily q is odd and has end digit 1, 3, 7 or 9
%D J.-P. Allouche, J. Shallit: Automatic Sequences, Theory, Applications, Generalizations, Cambridge University Press, 2003
%e 3^2=9, 239 = prime(52) => q(1) = 3
%e 359 = prime(72) => q(2) = 3
%e k=18, prime(18) = 61, 141^2 = 19881, 616719881 = prime(32151650) => q(18) = 141
%Y A000290, A030461, A030459, A030469, A171154, A174031, A174034
%K base,nonn,uned
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 15 2010
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