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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.)