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%I #16 Jun 06 2022 05:47:19
%S 2,4,6,10,12,16,18,22,25,28,30,33,36,40,42,46,48,50,52,54,58,60,64,66,
%T 68,70,72,75,78,82,85,88,93,96,98,100,102,106,108,110,112,115,117,121,
%U 126,128,130,133,136,138,141,145,148,150,154,156,160,162,166,172,178,180,182
%N Numbers k such that P(k) < P(k+1) > P(k+2), where P(k) is the largest prime factor of k (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="/A082417/b082417.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>]
%F a(n) = A100392(n) - 1. - _T. D. Noe_, Nov 26 2007
%t gpf[n_] := FactorInteger[n][[-1, 1]]; ind = Position[Differences[Array[gpf, 200]], _?(# > 0 &)] // Flatten; ind[[Position[Differences[ind], _?(# > 1 &)] // Flatten]] (* _Amiram Eldar_, Jun 06 2022 *)
%Y Cf. A006530, A082418-A082422, A071869, A071870, A100392.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Apr 25 2003
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