A177435 The smallest prime p such that p//9_(n), its concatenation with n nines, is prime.

2, 5, 2, 5, 5, 2, 2, 7, 41, 5, 41, 41, 5, 23, 101, 13, 17, 29, 2, 37, 13, 5, 5, 79, 7, 19, 2, 5, 131, 47, 47, 103, 59, 5, 43, 89, 149, 71, 17, 5, 193, 29, 2, 277, 73, 107, 127, 79, 7, 103, 83, 19, 173, 29, 2, 23, 107, 103, 43, 47, 5, 13, 73, 503, 307, 197, 83, 113, 331, 163

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

Links

Table of n, a(n) for n=1..70.

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

Sequence in context: A082881 A104289 A309697 * A087272 A299963 A107060

Adjacent sequences: A177432 A177433 A177434 * A177436 A177437 A177438

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