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%I #23 Apr 10 2019 21:44:39
%S 8,14,20,24,32,38,44,48,54,62,68,74,80,84,90,98,104,110,114,128,132,
%T 140,152,158,164,168,174,182,194,200,212,224,230,234,242,252,258,264,
%U 272,278,284,294,308,314,318,332,338,350,354,360,368,374,380,384,390,398
%N First term in a sequence of at least 3 consecutive composite integers.
%C The meaning of "first" is that the run of composites is started with this term, that is, it is the one after a prime.
%C The number of terms in any run of composites is odd, because the difference between the relevant consecutive primes is even.
%C Composite numbers m such that m+1 is also composite, but m-1 is not. - _Reinhard Zumkeller_, Aug 04 2015
%H Harvey P. Dale, <a href="/A136798/b136798.txt">Table of n, a(n) for n = 1..1000</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_430.htm">Puzzle 430, Grimm's Conjecture</a>, Prime puzzles and problems connection.
%F a(n) = A049591(n)+1. - _R. J. Mathar_, Jan 23 2008
%F A010051(a(n)-1) * (1 - A010051(a(n)) - A010051(a(n)+1)) = 1. - _Reinhard Zumkeller_, Aug 04 2015
%e a(1)=8 because 8 is the first term in a sequential run of 3 composites, 8,9,10
%t Prime/@Flatten[Position[Differences[Prime[Range[80]]],_?(#>2&)]]+1 (* _Harvey P. Dale_, Jun 19 2013 *)
%o (Haskell)
%o import Data.List (elemIndices)
%o a136798 n = a136798_list !! (n-1)
%o a136798_list = tail $ map (+ 1) $ elemIndices 1 $
%o zipWith (*) (0 : a010051_list) $ map (1 -) $ tail a010051_list
%o -- _Reinhard Zumkeller_, Aug 04 2015
%Y Cf. A136799, A136800, A136801.
%Y Cf. A049591, A010051.
%Y a(n) = 2 * A104280(n).
%K easy,nonn
%O 1,1
%A _Enoch Haga_, Jan 21 2008
%E Edited by _R. J. Mathar_, May 27 2009