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A174031 The smallest integer k>0 such that the double-concatenation 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

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

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Last modified July 2 15:56 EDT 2020. Contains 335404 sequences. (Running on oeis4.)