cp's OEIS Frontend

A136798 First term in a sequence of at least 3 consecutive composite integers.

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