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A124247 Numbers n such that n!!-8 and n!!+8 are two consecutive primes. 0
41, 91, 299, 341 (list; graph; refs; listen; history; text; internal format)
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[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
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Nov 19 2006
STATUS
approved

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Last modified July 20 05:30 EDT 2024. Contains 374441 sequences. (Running on oeis4.)