OFFSET
1,1
COMMENTS
Erdős conjectured that this sequence is infinite.
Balog (2001) proved that this sequence is infinite. - Amiram Eldar, Aug 02 2020
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Antal Balog, On triplets with descending largest prime factors, Studia Scientiarum Mathematicarum Hungarica, Vol. 38, No. 1-4 (2001), pp. 45-50.
P. Erdős and C. Pomerance, On the largest prime factors of n and n+1, Aequationes Math. 17 (1978), pp. 311-321. [alternate link]
Sungjin Kim, Two Remarks on the Largest Prime Factors of n and n+1, J. of Integer Sequences, 23 (2020), #20.10.1.
EXAMPLE
13 is a term since gpf(13) = 13, gpf(14) = 7, gpf(15) = 5, and 13 > 7 > 5.
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, ", ")))
(PARI) gpf(n) = vecmax(factor(n)[, 1]);
isok(k) = (gpf(k) > gpf(k+1)) && (gpf(k+1) > gpf(k+2)); \\ Michel Marcus, Nov 02 2020
(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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jun 09 2002
STATUS
approved