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

1,1

Comments

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(PARI) is(p)=isprime((p-1)\2)&&isprime((p+3)\2)&&isprime(p) \\ Charles R Greathouse IV, Apr 18 2013
(Magma) [p: p in PrimesUpTo(13000)|IsPrime((p-1) div 2) and IsPrime((p+3) div 2)]; // Marius A. Burtea, Jan 01 2020

Crossrefs

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

Sequence in context: A111671 A213895 A140111 * A141305 A243916 A181841

Adjacent sequences: A118069 A118070 A118071 * A118073 A118074 A118075

Keyword

easy,nonn

Author

Jonathan Vos Post, May 11 2006

Extensions

More terms from Harvey P. Dale, Apr 04 2011

More terms from Amiram Eldar, Jan 01 2020

Status

approved