cp's OEIS Frontend

A173291 Smallest prime p such that the concatenation of p and prime(n) is a prime, or 0 if no other number exists.

%I A173291 #8 Jul 05 2014 01:07:37
%S A173291 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,
%T A173291 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,
%U A173291 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
%N A173291 Smallest prime p such that the concatenation of p and prime(n) is a prime, or 0 if no other number exists.
%C A173291 If prime(n) has k digits then a(k) is the smallest prime(m) where 10^k * prime(m) + prime(n) is a prime.
%C A173291 In base 10, no prime can be prefixed to 2 or 5 to make another prime.
%D A173291 John Derbyshire, Prime obsession. Joseph Henry Press, Washington, DC 2003
%D A173291 Marcus du Sautoy, Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004
%D A173291 Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005
%e A173291 a(2) = 2 because prime(2) = 3, and the concatenation of 2 and 3 gives the prime 23.
%e A173291 a(3) = 0 because prime(3) = 5 and there is no prime to concatenate with to give another prime.
%e A173291 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.
%Y A173291 Cf. A088606, A167764, A168327, A168417, A030469.
%K A173291 base,nonn
%O A173291 1,2
%A A173291 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 15 2010