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

1,1

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

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Sequence in context: A060255 A316791 A154552 * A352913 A100857 A100856

Adjacent sequences: A261460 A261461 A261462 * A261464 A261465 A261466

Keyword

nonn

Author

Harvey P. Dale, Aug 20 2015

Status

approved