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Search: id:A099154
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| A099154 |
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Largest number k such that the interval [k^2,(k+1)^2] contains not more than n pairs of twin primes. |
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1
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| 122, 213, 502, 545, 922, 950, 749, 1098, 1330, 1450, 1634, 1623, 2135, 2110, 2177, 2244, 2760, 2413, 2556, 3280, 3454, 3211, 3740, 3540, 4104, 4096, 4391, 4457, 4592, 5309, 4758, 5720, 5747, 5295, 5902, 5456, 5920, 6395, 5810, 7007, 7109, 7450, 7540
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The validity of this sequence depends on the twin prime conjecture.
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LINKS
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Eric Weisstein's World of Mathematics, Twin Primes.
Eric Weisstein's World of Mathematics, Twin Prime Conjecture.
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EXAMPLE
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a(1)=213 because the interval [213^2,214^2]=[45369,45796] contains one pair of twin primes (45587,45589) wheras all higher intervals are conjectured to contain at least two pairs of twin primes.
The interval [122^2,123^2]=[A091592(11)^2,(A091592(11)+1)^2] is conjectured to be the last interval between two consecutive squares containing no twin primes.
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CROSSREFS
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Cf. A091591 number of pairs of twin primes between n^2 and (n+1)^2, A091592 numbers n such that there are no twin primes between n^2 and (n+1)^2, A014574.
Sequence in context: A138026 A077030 A105983 this_sequence A158131 A004925 A070955
Adjacent sequences: A099151 A099152 A099153 this_sequence A099155 A099156 A099157
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 30 2004
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