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A103667
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Primes p such that the largest prime divisor of p-1 is greater than the largest prime divisor of p+1.
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8
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7, 11, 23, 29, 31, 47, 53, 59, 71, 79, 83, 89, 103, 107, 127, 131, 139, 149, 167, 173, 179, 191, 199, 223, 227, 233, 239, 263, 269, 293, 307, 311, 317, 347, 349, 359, 367, 373, 383, 389, 419, 431, 439, 449, 461, 467, 479, 499, 503, 509, 557, 563, 569, 571, 587
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OFFSET
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1,1
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COMMENTS
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Conjecture: this sequence is of positive relative density in the primes, perhaps even 1/2. - Charles R Greathouse IV, Dec 22 2022
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LINKS
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EXAMPLE
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a(1)=7 because the largest prime divisor of 6 is greater than the largest prime divisor of 8.
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MAPLE
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filter:= p -> isprime(p) and max(numtheory:-factorset(p-1)) > max(numtheory:-factorset(p+1)):
select(filter, [seq(i, i=3..1000, 2)]); # Robert Israel, Jan 15 2024
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MATHEMATICA
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Select[Prime@Range[2, 107], If[FactorInteger[#-1][[-1, 1]]>FactorInteger[#+1][[-1, 1]], True]&] (* James C. McMahon, Jan 15 2024 *)
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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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