A128551 a(n) = p, the lesser of twin primes (p, q=p+2) such that p*q - p - q is prime.

3, 5, 29, 71, 107, 191, 239, 569, 881, 1091, 1289, 1619, 1721, 1931, 1997, 2081, 2087, 2129, 2309, 2381, 2549, 2591, 2729, 3299, 3359, 3527, 3851, 4229, 4241, 4271, 4649, 5279, 5501, 5651, 6299, 7127, 7349, 7547, 7589, 7757, 8219, 8969, 9437, 10037

Offset: 1

Author

Zak Seidov, Mar 10 2007

Keywords

• nonn

Comments

Or, p prime such that p+2 and p^2-2 are primes.

Examples

			3, 5 and 3*5-3-5=7 are prime; 5, 7 and 5*7-5-7=23 are prime; 29, 31 and 29*31-29-31=839 are primes.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A096342, A126148, A128547, A128548, A128550.

Programs

Mathematica

Clear[lst,f1,f2,n,p]; f1[n_]:=PrimeQ[n+2]; f2[n_]:=PrimeQ[n*(n+2)-((n+2)+n)]; lst={};Do[p=Prime[n];If[f1[p]&&f2[p],AppendTo[lst,p]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 19 2009 *)
tpQ[{a_,b_}]:=b-a==2&&PrimeQ[a*b-a-b]; Transpose[Select[Partition[ Prime[ Range[ 1300]],2,1],tpQ]][[1]] (* Harvey P. Dale, May 22 2014 *)