%I #10 Sep 27 2013 15:38:51
%S 3,5,11,15,17,29,35,39,41,44,49,51,55,59,63,65,69,71,80,87,95,99,101,
%T 104,107,111,116,129,137,143,149,153,155,161,164,179,186,191,195,197,
%U 203,209,224,227,230,237,239,242,249,255,265,267,269,272,279,281,285,291,296,299
%N Numbers n such that P(n+1) < P(n) < P(n+2), where P(n) = largest prime factor of n (A006530).
%D Antal Balog, On the largest prime factor of consecutive integers, Abstracts Amer. Math. Soc., 25 (No. 2, 2002), p. 337, #975-11-76.
%H T. D. Noe, <a href="/A082421/b082421.txt">Table of n, a(n) for n = 1..1000</a>
%H P. Erdős and C. Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/PDF/paper17.pdf">On the largest prime factors of n and n+1</a>, Aequationes Math. 17 (1978), p. 311-321. [<a href="http://www.renyi.hu/~p_erdos/1978-29.pdf">alternate link</a>]
%t Flatten[Position[Partition[Table[FactorInteger[n][[-1,1]],{n,400}],3,1],_?(#[[2]]<#[[1]]<#[[3]]&),{1},Heads->False]] (* _Harvey P. Dale_, Sep 27 2013 *)
%Y Cf. A006530, A082417-A082422, A071869, A071870.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Apr 25 2003