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A071869
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Numbers k such that gpf(k) < gpf(k+1) < gpf(k+2) where gpf(k) denotes the largest prime factor of k.
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12
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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
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OFFSET
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1,1
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COMMENTS
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Erdős and Pomerance showed in 1978 that this sequence is infinite.
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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PROG
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(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:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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