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

1,1

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

Links

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

Example

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.

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

Crossrefs

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

Sequence in context: A032457 A122564 A162876 * A166564 A058595 A154773

Adjacent sequences: A162872 A162873 A162874 * A162876 A162877 A162878

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 15 2009

Status

approved