A186169 Consider two consecutive primes {p,q} such that {P=2p-q,Q=2q-p} are both prime. Sequence gives lesser primes p.

47, 257, 607, 619, 647, 1097, 1459, 1499, 1709, 1747, 1889, 2677, 2861, 3307, 3559, 4007, 5107, 5387, 5419, 6317, 6367, 7309, 7829, 9467, 10079, 10639, 11789, 12589, 12647, 12721, 13457, 14747, 15149, 15749, 15797, 15889, 15907, 17477, 17839, 18217, 19477

Offset: 1

Author

Zak Seidov, Aug 18 2012

Keywords

• nonn

Comments

Note that Q-P=3(q-p).

No common terms with A181848.

Examples

			a(1)=47 because p=47, q=53 and {P=41,Q=59} are both prime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A181848.

Programs

Mathematica

a = 2; Reap[ Do[b = Prime[n]; If[PrimeQ[2*a - b] && PrimeQ[2*b - a], Sow[a]]; a = b, {n, 2, 1000}]][[2, 1]]
Transpose[Select[Partition[Prime[Range[2500]],2,1],AllTrue[{2#[[1]]- #[[2]], 2#[[2]]-#[[1]]},PrimeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 14 2015 *)