

A174031


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


6



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

EvaMaria Zschorn (em.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



