OFFSET
1,1
COMMENTS
By definition, the lower member, here at the odd-indexed positions, is in A089188.
p+1 must be divisible by 4. - Robert Israel, Jul 24 2015
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
(179,181) are in the sequence because 179-1=2*89 is squarefree and 181+1=2*7*13 is also squarefree.
MAPLE
f:= p -> if isprime(p) and isprime(p+2) and numtheory:-issqrfree(p-1) and numtheory:-issqrfree(p+3) then (p, p+2) else NULL fi:
map(f, [4*k-1 $ k=1..1000]); # Robert Israel, Jul 24 2015
MATHEMATICA
f[n_]:=Module[{a=m=0}, Do[If[FactorInteger[n][[m, 2]]>1, a=1], {m, Length[FactorInteger[n]]}]; a]; lst={}; Do[p=Prime[n]; r=p+2; If[PrimeQ[r], If[f[p-1]==0&&f[r+1]==0, AppendTo[lst, p]; AppendTo[lst, r]]], {n, 7!}]; lst
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jul 15 2009
EXTENSIONS
Definition rephrased by R. J. Mathar, Jul 27 2009
STATUS
approved