A109945 Primes p such that [p,p+2] is a pair of twin primes and (p*(p+2)-1)/2 is prime.

3, 5, 11, 29, 41, 71, 137, 281, 461, 599, 641, 827, 881, 1091, 1301, 1607, 2129, 2267, 2381, 2687, 3527, 3557, 3581, 4127, 4229, 4337, 4547, 5009, 5741, 6131, 6791, 6959, 7211, 7487, 7547, 8009, 8597, 8861, 9041, 9281, 10007, 10037, 10427, 10889, 11117

Offset: 1

Author

Hugo Pfoertner, Jul 09 2005

Keywords

• nonn

Examples

			3 is in the sequence because [3,5] is a pair of twin primes and (3*5 - 1)/2=7 is prime.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086870 [corresponding primes], A093706 [primes p such that (p*nextprime(p)-1)/2 is prime], A061351 [number separating twin pair is squarefree].

Programs

Mathematica

lst={}; d=2; Do[p1=Prime[n]; p2=Prime[n+1]; If[p2-p1==2&&PrimeQ[(p1*p2-1)/2], AppendTo[lst, p1]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 08 2008 *)