Search: id:A108013
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%I A108013
%S A108013 3,5,149,179,239,269,419,569,1289,1319,2309,2549,2729,3359,3389,4259,
%T A108013 4649,5849,5879,6359,6779,8999,9239,9629,10529,10889,11969,13679,13829,
%U A108013 14009,14549,16229,16649,18059,18119,18539,19139,19379,21599,21839
%N A108013 Primes p such that p+2 and p(p+2)+2 are primes.
%C A108013 Except for the first 2 terms, these numbers all end in 9. Froof: Any 
               odd prime P>5 can have one of the following forms: 10k+1,10k+3,10k+7,
               10k+9. 10k+1 => p(p+2)+2 ends in 5 not prime so p <> form 10k+1 10k+3 
               => (p+2) ends in 5 not prime so p <> form 10k+3 10k+7 => p(p+2)+2 
               ends in 5 not prime so p <> form 10k+7 Thus p is of the form 10k+9 
               as stated. Moreover, p+2 ends in 1 and p(p+2)+2 is of the form 100h+1 
               since (10k+9)(10k+11)+2 = 100(k^2+2k+1)+1
%e A108013 149*151+2 = 22501. 149,151,22501 are prime so 149 is in the table.
%o A108013 (PARI) g(n,k) = forprime(x1=3,n, x2=x1+2; if(isprime(x2), p=x1*x2+k; 
               if(isprime(p), print1(x1",") ) ) )
%Y A108013 Cf. A051779.
%Y A108013 Sequence in context: A103993 A088269 A164371 this_sequence A087307 A038535 
               A090953
%Y A108013 Adjacent sequences: A108010 A108011 A108012 this_sequence A108014 A108015 
               A108016
%K A108013 easy,nonn
%O A108013 1,1
%A A108013 Cino Hilliard (hillcino368(AT)gmail.com), May 30 2005

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