A126655 Numbers n such that 6*p(n)-1 and 6*p(n)+1 are twin primes and 6*p(n+1)-1 and 6*p(n+1)+1 are also twin primes with p(n) = n-th prime.

1, 2, 3, 27, 137, 340, 479, 882, 1415, 1883, 3442, 3798, 4284, 5827, 7559, 8783, 9453, 10355, 10731, 11388, 12565, 13613, 16477, 17007, 18402, 18665, 19450, 19633, 22306, 24971, 25083, 29108, 29861, 30748, 31694, 32622, 33097, 36743, 37141

Offset

1,2

Links

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

Example

6*2-1=11 6*2+1=13 11 13 twin primes as 17 and 19 so 1 is first term of the sequence
6*3-1=17 6*3+1=19 17 19 twin primes as 29 and 31 so 2 is second term of the sequence
6*5-1=29 6*5+1=31 29 and 31 twin primes 5=3rd prime
6*7-1=41 6*7+1=43 41 and 43 twin primes 7=4th prime so 3 is the 3rd term of the sequence

Mathematica

Select[Range[39000], PrimeQ[6*Prime[ # ] - 1] && PrimeQ[6*Prime[ # ] + 1] && PrimeQ[6*Prime[ # + 1] - 1] && PrimeQ[6*Prime[ # + 1] + 1] &] (* Ray Chandler, Feb 11 2007 *)
Select[Range[40000], AllTrue[Flatten[{6*Prime[#]+{1, -1}, 6*Prime[#+1]+{1, -1}}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 27 2015 *)

Crossrefs

Cf. A060212.

Sequence in context: A143876 A184506 A126203 * A242520 A132533 A059089

Adjacent sequences: A126652 A126653 A126654 * A126656 A126657 A126658

Keyword

nonn

Author

Pierre CAMI, Feb 09 2007

Extensions

Corrected and extended by Ray Chandler, Feb 11 2007

Status

approved