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 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 (list; graph; refs; listen; history; text; internal format)
 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 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 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 15 2010 STATUS approved

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Last modified December 17 14:12 EST 2018. Contains 318201 sequences. (Running on oeis4.)