A162873 List of pairs (p,r) of twin primes p and r=p+2 such that p-1, p+1 and r+1 are all divisible by squares > 1.

17, 19, 149, 151, 197, 199, 269, 271, 521, 523, 809, 811, 881, 883, 1049, 1051, 1061, 1063, 1277, 1279, 1949, 1951, 1997, 1999, 2141, 2143, 2549, 2551, 2789, 2791, 2969, 2971, 3257, 3259, 3329, 3331, 3581, 3583, 3821, 3823, 4049, 4051, 4157, 4159, 4229, 4231

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 15 2009

Keywords

• nonn
• tabf

Examples

			(197,199) is a pair because all of 196, 198, and 200 are divisible by squares.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A089189, A089194, A162870, A162872

Programs

Mathematica

dsQ[n_] := Length[Select[FactorInteger[n][[All, 2]], # > 1 &]] > 0; Select[ Partition[ Prime[ Range[ 250]],2,1],#[[2]]-#[[1]]==2&&AllTrue[ #[[1]]+ {-1,1,3},dsQ]&]//Flatten (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 28 2018 *)

Extensions

Corrected and previous (incorrect) Mathematica program replaced by Harvey P. Dale, Nov 28 2018