Search: id:A063637
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%I A063637
%S A063637 2,7,13,19,23,31,37,47,53,67,83,89,109,113,127,131,139,157,167,181,199,
%T A063637 211,233,251,257,263,293,307,317,337,353,359,379,389,401,409,443,449,
%U A063637 467,479,487,491,499,503,509,541,557,563,571,577,587,631,647,653,677
%N A063637 Primes p such that p+2 is a semiprime.
%C A063637 Primes of form p*q - 2, where p and q are primes.
%C A063637 Union of A049002 and A115093. - T. D. Noe (noe(AT)sspectra.com), Mar 
               01 2006
%D A063637 J.-R. Chen, On the representation of a large even integer as the sum 
               of a prime and a product of at most two primes, Sci. Sinica 16 (1973), 
               157-176.
%H A063637 T. D. Noe, <a href="b063637.txt">Table of n, a(n) for n=1..1000</a>
%H A063637 P. Pollack, <a href="http://www.math.dartmouth.edu/~ppollack/notes.pdf">
               Analytic and Combinatorial Number Theory</a> Course Notes, p. 146.
%H A063637 T. Tao, <a href="http://arXiv.org/abs/math.NT/0505402">Obstructions to 
               uniformity and arithmetic patterns in the primes</a>
%t A063637 f[n_] := Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[ n]]; 
               Select[ Prime[ Range[ 123]], f[ # + 2] == 2 &] (from Robert G. Wilson 
               v (rgwv(AT)rgwv.com), Apr 30 2005)
%o A063637 (PARI) { n=0; for (m=1, 10^9, p=prime(m); if (bigomega(p + 2) == 2, write("b063637.txt", 
               n++, " ", p); if (n==1000, break)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Aug 26 2009]
%Y A063637 Cf. A005383, A001358, A063638.
%Y A063637 a(n) = A062721(n) - 2.
%Y A063637 Cf. A109611 (Chen primes)
%Y A063637 Sequence in context: A007821 A156007 A067774 this_sequence A020623 A109346 
               A138646
%Y A063637 Adjacent sequences: A063634 A063635 A063636 this_sequence A063638 A063639 
               A063640
%K A063637 nonn
%O A063637 1,1
%A A063637 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 21 2001

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