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A162876 Twin prime pairs p, p+2 such that p-1 and p+3 are both squarefree.

%I A162876 #10 Dec 11 2019 07:17:46
%S A162876 3,5,11,13,59,61,71,73,107,109,179,181,191,193,227,229,311,313,419,
%T A162876 421,431,433,599,601,659,661,827,829,1019,1021,1031,1033,1091,1093,
%U A162876 1319,1321,1427,1429,1487,1489,1607,1609,1619,1621,1787,1789,1871,1873,1931
%N A162876 Twin prime pairs p, p+2 such that p-1 and p+3 are both squarefree.
%C A162876 By definition, the lower member, here at the odd-indexed positions, is in A089188.
%C A162876 p+1 must be divisible by 4. - _Robert Israel_, Jul 24 2015
%H A162876 Robert Israel, <a href="/A162876/b162876.txt">Table of n, a(n) for n = 1..10000</a>
%F A162876 {(p,p+2) : p in A001359, and p-1 in A005117, and p+3 in A005117}.
%e A162876 (179,181) are in the sequence because 179-1=2*89 is squarefree and 181+1=2*7*13 is also squarefree.
%p A162876 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:
%p A162876 map(f, [4*k-1 $ k=1..1000]); # _Robert Israel_, Jul 24 2015
%t A162876 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
%Y A162876 Cf. A089189, A089194, A162870, A162872, A162873, A162874, A162875
%K A162876 nonn
%O A162876 1,1
%A A162876 _Vladimir Joseph Stephan Orlovsky_, Jul 15 2009
%E A162876 Definition rephrased by _R. J. Mathar_, Jul 27 2009