OFFSET
1,1
COMMENTS
a(n) is the smallest prime p such that 10^n*(p+1)-1 is a prime number.
(a) if a(n) = 29 then a(n+1) = 2, (b) if a(n) = 59 and a(n+1) > 2 then a(n+1) = 5, etc.
(c) if a(n) = 19 then a(n+1) >= 2, as 1 is not a prime.
The smallest prime that is not appearing as such a concatenation seems to be 11:
The cases 11//9_(n) with n even, that is 11//9_(2*k), are multiples of 11 and ruled out.
Most cases 11//9_(n) with n odd are also ruled out:
11//9_(6*k+1) are multiples of 7. 11//9_(6*k+3) are multiples of 13.
It seems where 11//9_(6*k+5) is prime, so is 5//9_(6*k+5).
REFERENCES
M. du Sautoy: Die Musik der Primzahlen: Auf den Spuren des groessten Raetsels der Mathematik, Deutscher Taschenbuch Verlag, 2006
F. Ischebeck: Einladung zur Zahlentheorie, B.I. Wissenschaftsverlag, Mannheim-Leipzig-Wien-Zuerich, 1992
EXAMPLE
2//9 = 29 = prime(10), 2 = prime(1) is a(1).
5//99 = 599 = prime(109), 5 = prime(3) is a(2).
163//9_(70) is prime, so a(70)=163.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 08 2010
EXTENSIONS
Used variable n for the index; used more cautious wording for the unproved n=6k+5 case for the 11's - R. J. Mathar, May 10 2010
STATUS
approved