A174034 The smallest prime p such that the double-concatenation prime(n) // prime(n+1) // p is a prime number.

3, 3, 7, 19, 17, 7, 17, 7, 3, 23, 11, 11, 11, 17, 3, 3, 7, 3, 11, 17, 29, 19, 13, 7, 37, 7, 23, 37, 7, 23, 7, 7, 7, 11, 7, 53, 29, 31, 31, 13, 11, 17, 7, 11, 11, 29, 23, 47, 7, 7, 7, 13, 11, 19, 67, 19, 13, 101, 59, 13, 13, 31, 17, 23, 7, 13, 29, 73, 29, 7

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 06 2010

Keywords

• base
• nonn

Comments

It is conjectured that a(n) = 3 for infinitely many n.

Examples

			n=1: 2 // 3 // 3 = 233, which is prime, so a(1) = 3.
n=2: 3 // 5 // 2 = 352, which is not prime, but 3 // 5 // 3 = 353 is, so a(2) = 3.
		

Crossrefs

Cf. A030461, A030459, A030469, A171154, A174031

Programs

PARI

A174034(n)={ n=eval(Str(prime(n),prime(n+1))); for( d=1,99, n*=10; forprime( p=10^(d-1),10^d, isprime(n+p) & return(p)))} \\ M. F. Hasler, Dec 01 2010

Sage

concat = lambda xx: Integer(''.join(map(str,xx)))
A174034 = lambda x: next((p for p in Primes() if is_prime(concat([nth_prime(x), nth_prime(x+1), p])))) # D. S. McNeil, Dec 02 2010

Extensions

Edited and terms checked by D. S. McNeil, Dec 01 2010