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A091591
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Number of pairs of twin primes between n^2 and (n+1)^2.
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4
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1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 2, 1, 2, 2, 1, 1, 0, 2, 1, 1, 1, 2, 2, 0, 0, 3, 2, 0, 1, 3, 2, 0, 3, 2, 1, 3, 0, 3, 2, 1, 3, 2, 4, 2, 2, 3, 0, 2, 2, 4, 0, 2, 1, 1, 5, 4, 4, 1, 2, 3, 4, 3, 5, 2, 2, 3, 2, 4, 1, 2, 2, 3, 4, 3, 0, 3, 3, 2, 4, 5, 2, 2, 3, 4, 1, 2, 3, 2, 3, 3, 1, 5, 1, 3, 4, 4, 2, 5, 3, 4, 1, 3, 5, 1, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,8
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COMMENTS
| a(1) and a(2) are omitted because they are dependent on the treatment of the twin pair (3,5). It is conjectured that a(n)>0 for all n>122. Proving this would also prove the twin prime conjecture.
Proving a(n)>0 for n>122 would also prove Legendre's conjecture that there is a prime between n^2 and (n+1)^2. - T. D. Noe, Feb 28 2007
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LINKS
| T. D. Noe, Table of n, a(n) for n=3..10000
Eric Weisstein's World of Mathematics, Twin Prime Conjecture.
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EXAMPLE
| a(3)=1 because the interval [3^2,4^2] contains one pair of twins (11,13).
a(9)=0 because the interval [9^2,10^2] is one of the few known intervals (given in A091592) not containing twin primes.
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CROSSREFS
| Cf. A000290, A001359, A006512, A091592.
Cf. A014085 (number of primes between n^2 and (n+1)^2)
Sequence in context: A080121 A122901 A001917 * A109374 A079706 A078703
Adjacent sequences: A091588 A091589 A091590 * A091592 A091593 A091594
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 22 2004
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