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

41, 91, 299, 341

Offset: 1

Author

Farideh Firoozbakht, Nov 19 2006

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A076188.

Programs

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 *)