A174287 Smallest natural square base q = q(k) that concatenation prime(k)//prime(k+1)//q^2 (k = 1, 2, ...) is a prime number.

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, 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, 13, 21, 7, 7, 7, 1, 1, 43, 1, 1, 57, 1, 67, 7, 17

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 15 2010

Keywords

• base
• nonn
• uned

Comments

Note two consecutive primes prime(k)//prime(k+1)

Necessarily q is odd and has end digit 1, 3, 7 or 9

Examples

			3^2=9, 239 = prime(52) => q(1) = 3
359 = prime(72) => q(2) = 3
k=18, prime(18) = 61, 141^2 = 19881, 616719881 = prime(32151650) => q(18) = 141
		

References

• J.-P. Allouche, J. Shallit: Automatic Sequences, Theory, Applications, Generalizations, Cambridge University Press, 2003

Crossrefs

A000290, A030461, A030459, A030469, A171154, A174031, A174034