Search: id:A158866
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%I A158866
%S A158866 2,5,30,31,66,73,88,91,141,147,217,513,607,637,743,760,784,845,856,911,
%T A158866 920,938,949,958,994,1015,1031,1092,1150,1246,1373,1470,1553,1586,1768,
%U A158866 1814,1871,2017,2029,2129,2261,2271,2331,2370,2458,2488,2510,2545,2579
%N A158866 Indices of twin primes if the sum of these twin primes+1 is an upper 
               twin prime.
%C A158866 If the sum is a member of a twin prime pair, it always is the upper twin 
               prime member. [Proof:
%C A158866 Twin primes are sequentially of the form 6n-1 and 6n+1. Then adding
%C A158866 according to the condition, we get 6n-1+6n+1+1 = 12n+1. This implies 
               12n+1 is
%C A158866 an upper member since if it were a lower member, 12n+1+2 would be the 
               upper
%C A158866 member but 12n+3 is not prime contradicting the definition of a twin 
               prime.
%C A158866 Therefore 12n+1 must be an upper twin prime member as stated.]
%F A158866 {k: A054735(k)+1 = A006512(j), any j} - R. J. Mathar, Apr 06 2009
%e A158866 The 30th lower twin prime is 659. 659+661+1 = 1321, prime and 1319 is 
               too.
%e A158866 Then 1319 is the lower member of the twin prime pair (1319,1321). So 
               30 is in the sequence.
%o A158866 (PARI) gp > g(n)=for(x=1,n,y=2*twinl(x)+3;if(isprime(y)&&isprime(y-2), 
               print1(x",")))
%Y A158866 Cf. A158870.
%Y A158866 Sequence in context: A073833 A086383 A118612 this_sequence A101078 A109739 
               A163800
%Y A158866 Adjacent sequences: A158863 A158864 A158865 this_sequence A158867 A158868 
               A158869
%K A158866 nonn
%O A158866 1,1
%A A158866 Cino Hilliard (hillcino368(AT)hotmail.com), Mar 28 2009
%E A158866 Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2009

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