A124247 Numbers n such that n!!-8 and n!!+8 are two consecutive primes.

41, 91, 299, 341

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

Table of n, a(n) for n=1..4.

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[x-8]&&NextPrime[x-8]==x+8]; Select[Range[ 350], n8pQ] (* Harvey P. Dale, Jun 25 2013 *)

Crossrefs

Cf. A076188.

Sequence in context: A044179 A044560 A039469 * A256485 A260556 A142658

Adjacent sequences: A124244 A124245 A124246 * A124248 A124249 A124250

Keyword

nonn

Author

Farideh Firoozbakht, Nov 19 2006

Status

approved