OFFSET
1,1
COMMENTS
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
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Carlos Rivera, Puzzle 430, Grimm's Conjecture, Prime puzzles and problems connection.
FORMULA
a(n) = A049591(n)+1. - R. J. Mathar, Jan 23 2008
EXAMPLE
a(1)=8 because 8 is the first term in a sequential run of 3 composites, 8,9,10
MATHEMATICA
Prime/@Flatten[Position[Differences[Prime[Range[80]]], _?(#>2&)]]+1 (* Harvey P. Dale, Jun 19 2013 *)
PROG
(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
-- Reinhard Zumkeller, Aug 04 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Enoch Haga, Jan 21 2008
EXTENSIONS
Edited by R. J. Mathar, May 27 2009
STATUS
approved