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

1,1

Comments

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

Links

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

Example

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.

Prog

(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
(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

Crossrefs

Cf. A030461, A030459, A030469, A171154, A174031

Sequence in context: A221269 A202047 A036574 * A081486 A097334 A214496

Adjacent sequences: A174031 A174032 A174033 * A174035 A174036 A174037

Keyword

base,nonn

Author

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

Extensions

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

Status

approved