A109835 Primes connected to two primes by the (p+1)/2 and 2p-1 operators.

3, 37, 157, 661, 877, 997, 1237, 1657, 2137, 2557, 3061, 4177, 4261, 4357, 4621, 5581, 6037, 6121, 6217, 6361, 7537, 8317, 8461, 8521, 9241, 9277, 9721, 9901, 10837, 11497, 12241, 12421, 13417, 13681, 14737, 14821, 15121, 15277, 16417, 17257

Offset: 1

Author

Alexandre Wajnberg, Aug 31 2005

Keywords

• nonn

Comments

Primes involved in Cunningham chains of the second kind (2p-1) and not starting or ending them. A059455 is produced by the same rule, but "of the first kind (2p+1)".

Examples

			a(2)=37 is here because (37 + 1)/2 = 19 and 2*37 - 1 = 73 are both primes;
a(11)=3061 because 1531 -> 3061 -> 6121 through <2p-1> and all are primes;
a(11)=3061, a(18)=6121 and a(31)=12241 are here because they are inside the complete Cunningham chain of the second kind 1531 -> 3061 -> 6121 -> 12241 -> 24481.
		

Links

• Chris Caldwell's Prime Glossary, Cunningham chains.

Crossrefs

Cf. A059455, A005385.

Programs

Mathematica

Select[Prime[Range[5000]],PrimeQ[(#+1)/2]&&PrimeQ[2#-1]&] (* Vladimir Joseph Stephan Orlovsky, Nov 19 2010 *)