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A136798
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First term in a sequence of at least 3 consecutive composite integers.
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8
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8, 14, 20, 24, 32, 38, 44, 48, 54, 62, 68, 74, 80, 84, 90, 98, 104, 110, 114, 128, 132, 140, 152, 158, 164, 168, 174, 182, 194, 200, 212, 224, 230, 234, 242, 252, 258, 264, 272, 278, 284, 294, 308, 314, 318, 332, 338, 350, 354, 360, 368, 374, 380, 384, 390, 398
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OFFSET
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1,1
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COMMENTS
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The meaning of "first" is that the run of composites is started with this term, that is, it is the one after a prime.
The number of terms in any run of composites is odd, because the difference between the relevant consecutive primes is even.
Composite numbers m such that m+1 is also composite, but m-1 is not. - Reinhard Zumkeller, Aug 04 2015
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LINKS
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FORMULA
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EXAMPLE
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a(1)=8 because 8 is the first term in a sequential run of 3 composites, 8,9,10
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MATHEMATICA
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Prime/@Flatten[Position[Differences[Prime[Range[80]]], _?(#>2&)]]+1 (* Harvey P. Dale, Jun 19 2013 *)
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PROG
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(Haskell)
import Data.List (elemIndices)
a136798 n = a136798_list !! (n-1)
a136798_list = tail $ map (+ 1) $ elemIndices 1 $
zipWith (*) (0 : a010051_list) $ map (1 -) $ tail a010051_list
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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