A153196 - OEIS

%I #18 Sep 08 2022 08:45:39

%S 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,

%T 99,102,106,109,134,136,137,142,146,169,171,174,176,181,191,204,212,

%U 214,216,219,237,241,246,247,267,269,277,282,286,297,311,312,321,324,332

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

%C 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

%H Vincenzo Librandi, <a href="/A153196/b153196.txt">Table of n, a(n) for n = 1..2000</a>

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

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

%e For n = 0, 6*n+5 = 5 and 6*n+7 = 7 are twin primes;

%e for n = 99, 6*n+5 = 599 and 6*n+7 = 601 are twin primes.

%p 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

%t Select[Range[0, 350], PrimeQ[6 # + 5]&&PrimeQ[6 # + 7]&] (* _Vincenzo Librandi_, Apr 04 2013 *)

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

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

%Y Cf. A037074. - _Vincenzo Librandi_, Dec 26 2008

%K nonn,easy

%O 1,3

%A _Vincenzo Librandi_, Dec 20 2008

%E Edited and extended by _Klaus Brockhaus_, Dec 26 2008