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 A071870 Numbers n such that gpf(n) > gpf(n+1) > gpf(n+2) where gpf(x) denotes the largest prime factor of x. 12
 13, 14, 34, 37, 38, 43, 61, 62, 73, 79, 86, 94, 103, 118, 122, 123, 142, 151, 152, 157, 158, 163, 173, 185, 193, 194, 202, 206, 214, 218, 223, 229, 241, 254, 257, 258, 271, 277, 278, 283, 284, 295, 298, 302, 313, 317, 318, 321, 322, 326, 331, 334, 341, 373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Erdős conjectured that this sequence is infinite. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 P. Erdős and C. Pomerance, On the largest prime factors of n and n+1, Aequationes Math. 17 (1978), pp. 311-321. [alternate link] MATHEMATICA Select[ Range[400], FactorInteger[#][[-1, 1]] >  FactorInteger[# + 1][[-1, 1]] > FactorInteger[# + 2][[-1, 1]] &] (* Jean-François Alcover, Jun 17 2013 *) PROG (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, ", "))) (Python) from sympy import factorint A071870_list, p, q, r = [], 1, 2, 3 for n in range(2, 10**4):     p, q, r = q, r, max(factorint(n+2))     if p > q > r:         A071870_list.append(n) # Chai Wah Wu, Jul 24 2017 CROSSREFS Cf. A006530, A070087, A071869, A082417-A082422. Sequence in context: A167996 A308122 A292116 * A041350 A041348 A041346 Adjacent sequences:  A071867 A071868 A071869 * A071871 A071872 A071873 KEYWORD nonn AUTHOR Benoit Cloitre, Jun 09 2002 STATUS approved

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Last modified August 21 23:00 EDT 2019. Contains 326169 sequences. (Running on oeis4.)