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

1,1

Comments

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

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

References

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

Links

Table of n, a(n) for n=1..71.

Example

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

Crossrefs

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

Sequence in context: A185422 A131889 A292386 * A186826 A185418 A050609

Adjacent sequences: A174284 A174285 A174286 * A174288 A174289 A174290

Keyword

base,nonn,uned

Author

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

Status

approved