A118071 Primes which are the sum of a twin prime pair + 1.

13, 37, 61, 277, 397, 457, 541, 1201, 1237, 1321, 1621, 1657, 2557, 2857, 3217, 4057, 4177, 4261, 4621, 5101, 5581, 6337, 6661, 6781, 7057, 7537, 8101, 8317, 8461, 8521, 8677, 9277, 9601, 10837, 10957, 11317, 11701, 12541, 12601, 12721, 13381, 13921

Offset: 1

Author

Jonathan Vos Post, May 11 2006

Keywords

• easy
• nonn

Examples

			a(1) = 13 = 5 + 7 + 1 where (5,7) is a twin prime pair.
a(2) = 37 = 17 + 19 + 1.
a(3) = 61 = 29 + 31 + 1.
a(4) = 277 = 137 + 139 + 1.
a(5) = 397 = 197 + 199 + 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A000040, A001359, A006512, A054735, A038869.

Programs

Mathematica

Select[Total/@Select[Partition[Prime[Range[1000]],2,1],#[[2]]-#[[1]] == 2&]+1,PrimeQ] (* Harvey P. Dale, Jul 25 2019 *)

PARI

is(n)=n%12==1 && isprime(n) && isprime(n\2-1) && isprime(n\2+1) \\ Charles R Greathouse IV, Jan 21 2015

Formula

{A001359(k) + A006512(k) + 1} INTERSECT {A000040}.

{A054735(k) + 1} INTERSECT {A000040}.

{2*A001359(k) + 3} INTERSECT {A000040}.

{2*A006512(k) - 1} INTERSECT {A000040}. - Juri-Stepan Gerasimov, Apr 26 2010

Extensions

More terms added by Vladimir Joseph Stephan Orlovsky, Mar 10 2009