

A174287


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


0



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
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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



