A261463 Numbers n such that n is a twin prime and 2n + 1 is a twin prime.

3, 5, 29, 659, 809, 2129, 2549, 3329, 3389, 5849, 6269, 10529, 33179, 41609, 44129, 53549, 55439, 57329, 63839, 65099, 70379, 70979, 72269, 74099, 74759, 78779, 80669, 81929, 87539, 93239, 102299, 115469, 124769, 133979, 136949, 156419, 161459, 168449

Offset: 1

Author

Harvey P. Dale, Aug 20 2015

Keywords

• nonn

Comments

n is a Sophie Germain prime and a twin prime, and 2*n+1 is also a twin prime.

Apparently this contains 3 and the members of A069142. - R. J. Mathar, Aug 23 2015

Examples

			809 is a term because 809 and 811 are twin primes, and 2*809+1 = 1619 is a prime and a twin prime with 1621.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

sgtpQ[n_]:=Module[{sgp=2n+1},PrimeQ[sgp]&&AnyTrue[sgp+{2,-2},PrimeQ]]; Select[Union[Flatten[Select[Partition[Prime[Range[25000]],2,1], #[[2]]- #[[1]] ==2&]]],sgtpQ] (* The program uses the AnyTrue function from Mathematica version 10 *)
p=PrimeQ; Select[Prime@ Range[10^5], p[2#+1] && (p[#+2] || p[#-2]) && (p[2#+3] || p[2#-1]) &] (* Giovanni Resta, Aug 20 2015 *)

Formula

a(n+1) = A069142(n), n>=1. - G. C. Greubel, Aug 23 2015