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 A136798 First term in a sequence of at least 3 consecutive composite integers. 8
 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 (list; graph; refs; listen; history; text; internal format)
 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 A010051(a(n)-1) * (1 - A010051(a(n)) - A010051(a(n)+1)) = 1. - Reinhard Zumkeller, Aug 04 2015 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 Cf. A136799, A136800, A136801. Cf. A049591, A010051. a(n) = 2 * A104280(n). Sequence in context: A125163 A309355 A063288 * A172182 A091575 A091572 Adjacent sequences:  A136795 A136796 A136797 * A136799 A136800 A136801 KEYWORD easy,nonn AUTHOR Enoch Haga, Jan 21 2008 EXTENSIONS Edited by R. J. Mathar, May 27 2009 STATUS approved

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)