A174031 The smallest integer k>0 such that the double-concatenation prime(n) // prime(n+1) // k is a prime number.

3, 3, 1, 19, 1, 1, 1, 1, 1, 1, 9, 11, 11, 17, 3, 1, 1, 3, 11, 17, 21, 19, 1, 7, 37, 7, 23, 37, 7, 1, 7, 7, 7, 11, 7, 33, 29, 31, 1, 13, 11, 17, 7, 11, 11, 9, 9, 1, 7, 7, 1, 13, 11, 19, 67, 1, 13, 21, 49, 13, 13, 1, 1, 23, 1, 1, 29, 1, 29, 7

Offset

1,1

Comments

Leading zeros in k are not allowed.

All entries k are odd with final digit 1, 3, 7 or 9.

Dirichlet's prime number theorem for arithmetic progressions says that the sequence is infinite.

Conjecture: 1 appears infinitely often.

Links

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

Example

n=1: 2//3//1 = 231 = 3 * 7 * 11 is not prime, so k<>1. 233 = prime(51), therefore 3 is the first entry.
n=2: 3//5//1 = 351 = 3^3 * 13 is not prime, so k <> 1, but 353 = prime(71), therefore 3 is the second entry.
n=30: 113//127//1 = 1131271 = prime(87976), so the 30th entry is 1.

Maple

read("transforms") ;
A174031 := proc(n) for e from 1 do if isprime(digcatL([ithprime(n), ithprime(n+1), e])) then return e ; end if; end do: end proc:

Crossrefs

Cf. A030461, A030459, A030469, A171154

Sequence in context: A121438 A108391 A111840 * A228859 A259876 A276402

Adjacent sequences: A174028 A174029 A174030 * A174032 A174033 A174034

Keyword

base,nonn

Author

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

Extensions

Entries checked; replaced variables by OEIS standard names - R. J. Mathar, Nov 17 2010

Status

approved