%I A071538
%S A071538 0,0,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,
%T A071538 5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,
%U A071538 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
%N A071538 Number of twin prime pairs (p, p+2) with p <= n.
%C A071538 The convention is followed that a twin prime is <= n if its smaller member 
               is <= n.
%C A071538 Except for (3, 5), there is only 1 pair congruence class for twin primes, 
               i.e. (-1, +1) (mod 6). [From Daniel Forgues (squid(AT)zensearch.com), 
               Aug 05 2009]
%D A071538 S. Lang, The Beauty of Doing Mathematics, pp. 12-15; 21-22, Springer-Verlag 
               NY 1985.
%H A071538 Daniel Forgues, <a href="b071538.txt">Table of n, a(n) for n=1..99998</
               a>
%H A071538 Thomas R. Nicely, <a href="http://www.trnicely.net/">Some Results of 
               Computational Research in Prime Numbers</a>.
%H A071538 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TwinPrimes.html">Twin Primes</a>.
%e A071538 a(30)=5, since (29,31) is included along with (3,5), (5,7), (11,13) and 
               (17,19).
%o A071538 Contribution from M. F. Hasler (MHasler(AT)univ-ag.fr), Dec 10 2008: 
               (Start)
%o A071538 (PARI) A071538(n) = { local(s=0,L=0); forprime(p=3,n+2,L==p-2 & s++; 
               L=p); s }
%o A071538 /* For n > primelimit, one may use: */ A071538(n) = { local(s=isprime(2+n=precprime(n))&n,
               L); while( n=precprime(L=n-2),L==n & s++); s }
%o A071538 /* The following gives a reasonably good estimate for small and for large 
               values of n (cf. A007508): */
%o A071538 A071538est(n) = 1.320323631693739*intnum(t=2,n+1/n,1/log(t)^2)-log(n) 
               /* (The constant 1.320... is A114907.) */ (End)
%Y A071538 Cf. A007508, A033843, A001359, A006512.
%Y A071538 Sequence in context: A067099 A098429 A132090 this_sequence A138194 A133876 
               A152467
%Y A071538 Adjacent sequences: A071535 A071536 A071537 this_sequence A071539 A071540 
               A071541
%K A071538 nonn
%O A071538 1,5
%A A071538 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 30 2002
%E A071538 Definition edited by Daniel Forgues (squid(AT)zensearch.com), Jul 29 
               2009