Search: id:A109945
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%I A109945
%S A109945 3,5,11,29,41,71,137,281,461,599,641,827,881,1091,1301,1607,2129,2267,
%T A109945 2381,2687,3527,3557,3581,4127,4229,4337,4547,5009,5741,6131,6791,6959,
%U A109945 7211,7487,7547,8009,8597,8861,9041,9281,10007,10037,10427,10889,11117
%N A109945 Primes p such that [p,p+2] is a pair of twin primes and (p*(p+2)-1)/2 
               is prime.
%e A109945 a(1)=3 because [3,5] is a pair of twin primes and (3*5-1)/2=7 is prime.
%t A109945 lst={}; d=2; Do[p1=Prime[n]; p2=Prime[n+1]; If[p2-p1==2&&PrimeQ[(p1*p2-1)/
               2], AppendTo[lst, p1]], {n, 10^3}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Aug 08 2008]
%Y A109945 Cf. A086870 [corresponding primes], A093706 [primes p such that (p*nextprime(p)-1)/
               2 is prime], A061351 [number separating twin pair is square-free].
%Y A109945 Sequence in context: A032364 A088357 A093706 this_sequence A045536 A019338 
               A046134
%Y A109945 Adjacent sequences: A109942 A109943 A109944 this_sequence A109946 A109947 
               A109948
%K A109945 nonn
%O A109945 1,1
%A A109945 Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 09 2005

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