

A173291


Smallest prime p such that the concatenation of p and prime(n) is a prime, or 0 if no other number exists.


3



0, 2, 0, 3, 2, 3, 3, 7, 2, 2, 3, 3, 2, 7, 3, 3, 3, 7, 3, 2, 3, 3, 2, 3, 3, 5, 7, 5, 3, 2, 7, 2, 2, 19, 11, 7, 19, 3, 3, 9, 2, 3, 3, 7, 5, 37, 7, 31, 5, 3, 5, 2, 13, 2, 3, 41, 2, 3, 31, 2, 7, 2, 3, 2, 3, 11, 3, 13, 2, 7, 11, 3, 13, 3, 19, 2, 2, 13, 17, 37, 5, 13, 5, 3, 139, 5, 3, 3, 3, 3, 2, 5, 7, 3, 3
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OFFSET

1,2


COMMENTS

If prime(n) has k digits then a(k) is the smallest prime(m) where 10^k * prime(m) + prime(n) is a prime.
In base 10, no prime can be prefixed to 2 or 5 to make another prime.


REFERENCES

John Derbyshire, Prime obsession. Joseph Henry Press, Washington, DC 2003
Marcus du Sautoy, Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004
Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005


LINKS

Table of n, a(n) for n=1..95.


EXAMPLE

a(2) = 2 because prime(2) = 3, and the concatenation of 2 and 3 gives the prime 23.
a(3) = 0 because prime(3) = 5 and there is no prime to concatenate with to give another prime.
a(4) = 3 because prime(5) = 7 but the concatenation with 2 gives 27 = 3^3, so it has to be 3 in order to give 37, which is prime.


CROSSREFS

Cf. A088606, A167764, A168327, A168417, A030469.
Sequence in context: A277890 A243403 A051613 * A077961 A077962 A078031
Adjacent sequences: A173288 A173289 A173290 * A173292 A173293 A173294


KEYWORD

base,nonn


AUTHOR

EvaMaria Zschorn (em.zschorn(AT)zaschendorf.km3.de), Feb 15 2010


STATUS

approved



