

A124247


Numbers n such that n!!8 and n!!+8 are two consecutive primes.


0




OFFSET

1,1


COMMENTS

n is in the sequence iff n!!8 and n!!+8 are primes and the four numbers n!!2,n!!+2, n!!4 & n!!+4 are composites. It's interesting that related to the term 341 we can say 341!!(3+4+1) and 341!!+(3+4+1) are two consecutive primes with length 341+prime(3+4+1). Conjecture: 341 is the largest term of this sequence.


LINKS



EXAMPLE

341 is in the sequence because 341!!8 and 341!!+8 are primes and the four numbers 341!!2, 341!!+2, 341!!4 & 341!!+4 are composites.


MATHEMATICA

Select[Range[5, 500], PrimeQ[ #!!8]&&PrimeQ[ #!!+8]&&!PrimeQ[ #!!4] &&!PrimeQ[ #!!+4]&&!PrimeQ[ #!!2]&&!PrimeQ[ #!!+2]&]
n8pQ[n_]:=Module[{x=n!!}, PrimeQ[x8]&&NextPrime[x8]==x+8]; Select[Range[ 350], n8pQ] (* Harvey P. Dale, Jun 25 2013 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



