A118072 Primes which are the sum of a twin prime pair - 1.

7, 11, 23, 59, 83, 359, 383, 479, 563, 839, 863, 1283, 1319, 1619, 2039, 2063, 2099, 2459, 2579, 2903, 2963, 3863, 4259, 4283, 4679, 5099, 5939, 6599, 6659, 6719, 6779, 7079, 7643, 7703, 8039, 8543, 8963, 10463, 10559, 10883, 11003, 11279, 11483, 11699, 12263

Offset: 1

Author

Jonathan Vos Post, May 11 2006

Keywords

• easy
• nonn

Comments

Dickson's conjecture implies this sequence is infinite. - Charles R Greathouse IV, Apr 18 2013

Examples

			a(1) = 7 = 3 + 5 - 1 where (3,5) is a twin prime pair.
a(2) = 11 = 5 + 7 - 1 where (5,7) is a twin prime pair.
		

Links

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

Crossrefs

Cf. A000040, A001359, A005384, A006512, A054735.

Programs

Magma

[p: p in PrimesUpTo(13000)|IsPrime((p-1) div 2) and IsPrime((p+3) div 2)]; // Marius A. Burtea, Jan 01 2020

Mathematica

Select[(Total[#]-1)&/@Select[Partition[Prime[Range[500]],2,1], Last[#]- First[#]== 2&],PrimeQ]  (* Harvey P. Dale, Apr 04 2011 *)

PARI

is(p)=isprime((p-1)\2)&&isprime((p+3)\2)&&isprime(p) \\ Charles R Greathouse IV, Apr 18 2013

Formula

{A001359(k) + A006512(k) - 1} INTERSECT {A000040}. {A054735(k) - 1} INTERSECT {A000040}. {2*A001359(k) + 1} INTERSECT {A000040}.

Extensions

More terms from Harvey P. Dale, Apr 04 2011

More terms from Amiram Eldar, Jan 01 2020