A162875 Twin primes p and r such that p - 1, p + 1 and r + 1 are cubefree.

3, 5, 11, 13, 59, 61, 179, 181, 227, 229, 347, 349, 419, 421, 659, 661, 827, 829, 1019, 1021, 1091, 1093, 1427, 1429, 1451, 1453, 1667, 1669, 1787, 1789, 1931, 1933, 2027, 2029, 2339, 2341, 3299, 3301, 3371, 3373, 3467, 3469, 3539, 3541, 3851, 3853, 4019

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 15 2009

Keywords

• nonn

Comments

Apart from the first two terms, a(2n+1) = 11 mod 24 and a(2n) = 13 (mod 24). - Charles R Greathouse IV, Oct 12 2009

Examples

			179 and 181 are in the sequence because they are twin primes and 178 = 2*89, 180 = 2^2*3^2*5, 182 = 2*7*13 have no factors that are cubes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A089189, A089194, A162870, A162872, A162873, A162874.

Programs

Mathematica

f[n_]:=Module[{a=m=0},Do[If[FactorInteger[n][[m,2]]>2,a=1],{m,Length[FactorInteger[n]]}];a]; lst={};Do[p=Prime[n];r=p+2;If[PrimeQ[r],If[f[p-1]==0&&f[p+1]==0&&f[r+1]==0,AppendTo[lst,p];AppendTo[lst,r]]],{n,2*6!}];lst