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Search: id:A071538
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| A071538 |
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Number of twin prime pairs (p, p+2) with p <= n. |
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+0
15
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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The convention is followed that a twin prime is <= n if its smaller member is <= n.
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]
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REFERENCES
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S. Lang, The Beauty of Doing Mathematics, pp. 12-15; 21-22, Springer-Verlag NY 1985.
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1..99998
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers.
Eric Weisstein's World of Mathematics, Twin Primes.
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EXAMPLE
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a(30)=5, since (29,31) is included along with (3,5), (5,7), (11,13) and (17,19).
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PROGRAM
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Contribution from M. F. Hasler (MHasler(AT)univ-ag.fr), Dec 10 2008: (Start)
(PARI) A071538(n) = { local(s=0, L=0); forprime(p=3, n+2, L==p-2 & s++; L=p); s }
/* 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 }
/* The following gives a reasonably good estimate for small and for large values of n (cf. A007508): */
A071538est(n) = 1.320323631693739*intnum(t=2, n+1/n, 1/log(t)^2)-log(n) /* (The constant 1.320... is A114907.) */ (End)
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CROSSREFS
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Cf. A007508, A033843, A001359, A006512.
Sequence in context: A067099 A098429 A132090 this_sequence A138194 A133876 A152467
Adjacent sequences: A071535 A071536 A071537 this_sequence A071539 A071540 A071541
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 30 2002
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EXTENSIONS
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Definition edited by Daniel Forgues (squid(AT)zensearch.com), Jul 29 2009
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