A153196 Numbers n such that 6*n+5 and 6*n+7 are twin primes.

0, 1, 2, 4, 6, 9, 11, 16, 17, 22, 24, 29, 31, 32, 37, 39, 44, 46, 51, 57, 69, 71, 76, 86, 94, 99, 102, 106, 109, 134, 136, 137, 142, 146, 169, 171, 174, 176, 181, 191, 204, 212, 214, 216, 219, 237, 241, 246, 247, 267, 269, 277, 282, 286, 297, 311, 312, 321, 324, 332

Offset: 1

Author

Vincenzo Librandi, Dec 20 2008

Keywords

• nonn
• easy

Comments

Appears to be the partial sums of A160273 which are the successive differences (divided by 3) of the average of twin prime pairs divided by 2 (A040040). - Stephen Crowley, May 24 2009

Examples

			For n = 0, 6*n+5 = 5 and 6*n+7 = 7 are twin primes;
for n = 99, 6*n+5 = 599 and 6*n+7 = 601 are twin primes.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A001359 (lesser of twin primes), A002822 (6n-1, 6n+1 are twin primes).

Cf. A037074. - Vincenzo Librandi, Dec 26 2008

Programs

Magma

[ n: n in [0..335] | IsPrime(6*n+5) and IsPrime(6*n+7) ];

Maple

ZL := []; for p to 1000000 do if `and`(isprime(p), isprime(p+2)) then ZL := [op(ZL), ((p+2)^2-p^2)*(1/8)] end if end do; A160273 := [seq((ZL[i+1]-ZL[i])*(1/3), i = 2 .. nops(ZL)-1)]: ListTools[PartialSums]( A160273 ); # Stephen Crowley, May 24 2009

Mathematica

Select[Range[0, 350], PrimeQ[6 # + 5]&&PrimeQ[6 # + 7]&] (* Vincenzo Librandi, Apr 04 2013 *)

Formula

a(j) = (A001359(j+1)-5)/6.

a(j) = A002822(j)-1.

Extensions

Edited and extended by Klaus Brockhaus, Dec 26 2008