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A174034 The smallest prime p such that the double-concatenation prime(n) // prime(n+1) // p is a prime number. 2
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 (list; graph; refs; listen; history; text; internal format)
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) # [D. S. McNeil, Dec 02 2010]

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]))))

(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

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Last modified April 20 08:45 EDT 2019. Contains 322306 sequences. (Running on oeis4.)