A162876 Twin prime pairs p, p+2 such that p-1 and p+3 are both squarefree.
3, 5, 11, 13, 59, 61, 71, 73, 107, 109, 179, 181, 191, 193, 227, 229, 311, 313, 419, 421, 431, 433, 599, 601, 659, 661, 827, 829, 1019, 1021, 1031, 1033, 1091, 1093, 1319, 1321, 1427, 1429, 1487, 1489, 1607, 1609, 1619, 1621, 1787, 1789, 1871, 1873, 1931
Offset: 1
Keywords
Examples
(179,181) are in the sequence because 179-1=2*89 is squarefree and 181+1=2*7*13 is also squarefree.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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
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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
Extensions
Definition rephrased by R. J. Mathar, Jul 27 2009
Comments