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A099154 Largest number k such that the interval [k^2,(k+1)^2] contains not more than n pairs of twin primes. 0
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; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The terms of this sequence are conjectural, even under the twin prime conjecture.
LINKS
Eric Weisstein's World of Mathematics, Twin Primes.
Eric Weisstein's World of Mathematics, Twin Prime Conjecture.
EXAMPLE
a(1)=213 because the interval [213^2,214^2]=[45369,45796] contains one pair of twin primes (45587,45589) whereas 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.
CROSSREFS
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: A222578 A105983 A356369 * A304605 A158131 A004925
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Sep 30 2004
STATUS
approved

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)