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%I #30 Feb 24 2024 01:15:23
%S 7,11,23,59,83,359,383,479,563,839,863,1283,1319,1619,2039,2063,2099,
%T 2459,2579,2903,2963,3863,4259,4283,4679,5099,5939,6599,6659,6719,
%U 6779,7079,7643,7703,8039,8543,8963,10463,10559,10883,11003,11279,11483,11699,12263
%N Primes which are the sum of a twin prime pair - 1.
%C Dickson's conjecture implies this sequence is infinite. - _Charles R Greathouse IV_, Apr 18 2013
%H Amiram Eldar, <a href="/A118072/b118072.txt">Table of n, a(n) for n = 1..10000</a>
%F {A001359(k) + A006512(k) - 1} INTERSECT {A000040}. {A054735(k) - 1} INTERSECT {A000040}. {2*A001359(k) + 1} INTERSECT {A000040}.
%e a(1) = 7 = 3 + 5 - 1 where (3,5) is a twin prime pair.
%e a(2) = 11 = 5 + 7 - 1 where (5,7) is a twin prime pair.
%t Select[(Total[#]-1)&/@Select[Partition[Prime[Range[500]],2,1], Last[#]- First[#]== 2&],PrimeQ] (* _Harvey P. Dale_, Apr 04 2011 *)
%o (PARI) is(p)=isprime((p-1)\2)&&isprime((p+3)\2)&&isprime(p) \\ _Charles R Greathouse IV_, Apr 18 2013
%o (Magma) [p: p in PrimesUpTo(13000)|IsPrime((p-1) div 2) and IsPrime((p+3) div 2)]; // _Marius A. Burtea_, Jan 01 2020
%Y Cf. A000040, A001359, A005384, A006512, A054735.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, May 11 2006
%E More terms from _Harvey P. Dale_, Apr 04 2011
%E More terms from _Amiram Eldar_, Jan 01 2020
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