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A182426
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Lengths of runs of consecutive isolated primes beginning with A166251(n).
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5
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2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 3, 2, 1, 2, 1, 2, 1, 4, 3, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 3, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 2, 1, 3, 2, 1
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OFFSET
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1,1
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COMMENTS
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Theorem. If the sequence is unbounded, then there exist arbitrarily long sequences of consecutive primes p_k, p_(k+1),...,p_m such that every interval (p_i/2, p_(i+1)/2), i=k,k+1,...,m-1, contains a prime.
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LINKS
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PROG
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(Haskell)
import Data.List (group)
a182426 n = a182426_list !! (n-1)
a182426_list = concatMap f $ group $ zipWith (-) (tail ips) ips where
f xs | head xs == 1 = reverse $ enumFromTo 2 $ length xs + 1
| otherwise = take (length xs) $ repeat 1
ips = map a049084 a166251_list
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Data corrected: a(49)=2.
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STATUS
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approved
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