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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.)