A092993 Smallest prime of the form concatenation(s) of prime(n) with itself followed by a 3, or 0 if no such prime exists.

23, 0, 53, 73, 113, 13131313133, 173, 193, 233, 293, 313, 373, 41413, 433, 47474747474747474747474747473, 53535353535353535353535353533, 593, 613, 673, 71713, 733, 0, 83833, 89898989893, 97973, 1013, 1033, 1071071071073, 1093

Offset

1,1

Comments

Start with p=prime(n). If concat(p,3) is prime, then this is a(n), else consider concat(p,p,3), and so on.

Links

Table of n, a(n) for n=1..29.

Example

For a(1), start with prime(1)=2. Since appending a digit 3 yields the prime 23, a(1)=23.
For a(2), start with prime(2)=3. Since concatenating any number of digits '3' never yields a prime, a(2)=0.
For a(6), starting with prime(6)=13, one has to take 5 concatenations of itself before a prime is obtained when a final digit '3' is appended, thus a(6)=13131313133.
a(22)=0 since the concatenation of prime(22)=79 with itself, followed by a 3, is always composite. - Giovanni Resta, Apr 07 2006

Crossrefs

Cf. A092992, A092994, A092995.

Sequence in context: A180729 A119566 A143196 * A238331 A114784 A141517

Adjacent sequences: A092990 A092991 A092992 * A092994 A092995 A092996

Keyword

base,nonn

Author

Amarnath Murthy, Mar 28 2004

Extensions

a(15)-a(21) from Stefan Steinerberger, Nov 09 2005

More terms from Giovanni Resta, Apr 07 2006

Status

approved