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

1,3

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

Links

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

Formula

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

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Cf. A037074. - Vincenzo Librandi, Dec 26 2008

Sequence in context: A303331 A233776 A195526 * A247185 A237685 A220768

Adjacent sequences: A153193 A153194 A153195 * A153197 A153198 A153199

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 20 2008

Extensions

Edited and extended by Klaus Brockhaus, Dec 26 2008

Status

approved