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Numbers k such that 6*p(k)*p(k+1)*p(k+2)*p(k+3)*p(k+4)*p(k+5)-1 and 6*p(k)*p(k+1)*p(k+2)*p(k+3)*p(k+4)*p(k+5)+1 are twin primes with p(h) = h-th prime.
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%I #20 Jan 26 2020 11:06:21

%S 1,185,287,296,1372,1959,2531,3630,5393,6332,7210,7315,8108,8258,8794,

%T 9340,9989,11270,11706,12213,13494,13710,14246,14402,18188,19010,

%U 19075,20179,21394,22483,24256,24309,25070,26284,26634,30578,31799,32351,32652,33390

%N Numbers k such that 6*p(k)*p(k+1)*p(k+2)*p(k+3)*p(k+4)*p(k+5)-1 and 6*p(k)*p(k+1)*p(k+2)*p(k+3)*p(k+4)*p(k+5)+1 are twin primes with p(h) = h-th prime.

%H Amiram Eldar, <a href="/A129311/b129311.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Giovanni Resta)

%e 6*2*3*5*7*11*13-1=180179 prime, 180179+2=180181 twin prime of 180179, so n(1)=1.

%t PrimePi[Part[#, 1, 1] & /@ FactorInteger /@ Select[Times @@@ Partition[ Prime[Range[5 10^4]], 6, 1], PrimeQ[6 # + 1] && PrimeQ[6 # - 1] &]] (* _Giovanni Resta_, Sep 16 2019 *)

%Y Cf. A129310, A129313.

%K nonn

%O 1,2

%A _Pierre CAMI_, Apr 09 2007

%E More terms from _Giovanni Resta_, Sep 16 2019