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

Author

Amarnath Murthy, Mar 28 2004

Keywords

• base
• nonn

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.

Examples

			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.

Extensions

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

More terms from Giovanni Resta, Apr 07 2006