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A071869 Numbers n such that gpf(n) < gpf(n+1) < gpf(n+2) where gpf(x) denotes the largest prime factor of x. 12

%I

%S 8,9,20,21,24,27,32,45,56,57,77,81,84,90,91,92,105,114,120,125,132,

%T 135,140,144,147,165,168,169,170,171,175,176,177,189,200,204,212,216,

%U 220,221,225,231,234,235,247,252,260,261,275,288,289,300,315,324,345,354

%N Numbers n such that gpf(n) < gpf(n+1) < gpf(n+2) where gpf(x) denotes the largest prime factor of x.

%C Erdős and Pomerance showed in 1978 that this sequence is infinite.

%H T. D. Noe, <a href="/A071869/b071869.txt">Table of n, a(n) for n = 1..1000</a>

%H P. Erdős and C. Pomerance, <a href="http://www.renyi.hu/~p_erdos/1978-29.pdf">On the largest prime factors of n and n+1</a>, Aequationes Math. 17 (1978), p. 311-321.

%F a(n) = A079747(n+1) - 1. - _T. D. Noe_, Nov 26 2007

%o (PARI) for(n=2,500,if(sign(component(component(factor(n),1),omega(n))-component(component(factor(n+1),1),omega(n+1)))+sign(component(component(factor(n+1),1),omega(n+1))-component(component(factor(n+2),1),omega(n+2)))==-2,print1(n,",")))

%o (Python)

%o from sympy import factorint

%o A071869_list, p, q, r = [], 1, 2, 3

%o for n in range(2,10**4):

%o p, q, r = q, r, max(factorint(n+2))

%o if p < q < r:

%o A071869_list.append(n) # _Chai Wah Wu_, Jul 24 2017

%Y Cf. A006530, A070089, A071870, A082417-A082422.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jun 09 2002

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Last modified September 18 07:49 EDT 2019. Contains 327168 sequences. (Running on oeis4.)