

A153196


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


2



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
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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)^2p^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 (6n1, 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



