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Numbers n such that P(n+1) < P(n) < P(n+2), where P(n) = largest prime factor of n (A006530).
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%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