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A071869
Numbers k such that gpf(k) < gpf(k+1) < gpf(k+2) where gpf(k) denotes the largest prime factor of k.
12
8, 9, 20, 21, 24, 27, 32, 45, 56, 57, 77, 81, 84, 90, 91, 92, 105, 114, 120, 125, 132, 135, 140, 144, 147, 165, 168, 169, 170, 171, 175, 176, 177, 189, 200, 204, 212, 216, 220, 221, 225, 231, 234, 235, 247, 252, 260, 261, 275, 288, 289, 300, 315, 324, 345, 354
OFFSET
1,1
COMMENTS
Erdős and Pomerance showed in 1978 that this sequence is infinite.
LINKS
Paul Erdős and Carl Pomerance, On the largest prime factors of n and n+1, Aequationes Math. 17 (1978), pp. 311-321.
FORMULA
a(n) = A079747(n+1) - 1. - T. D. Noe, Nov 26 2007
MATHEMATICA
gpf[n_] := FactorInteger[n][[-1, 1]]; ind = Position[Differences[Array[gpf, 350, 2]], _?(# > 0 &)] // Flatten; ind[[Position[Differences[ind], 1] // Flatten]] + 1 (* Amiram Eldar, Jun 05 2022 *)
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
A071869_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:
A071869_list.append(n) # Chai Wah Wu, Jul 24 2017
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jun 09 2002
STATUS
approved