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A103667
Primes p such that the largest prime divisor of p-1 is greater than the largest prime divisor of p+1.
8
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
OFFSET
1,1
COMMENTS
Primes of the form 2*A070087(n)+1 for some n. - Charles R Greathouse IV, Dec 22 2022
Conjecture: this sequence is of positive relative density in the primes, perhaps even 1/2. - Charles R Greathouse IV, Dec 22 2022
LINKS
EXAMPLE
a(1)=7 because the largest prime divisor of 6 is greater than the largest prime divisor of 8.
MAPLE
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
MATHEMATICA
Select[Prime@Range[2, 107], If[FactorInteger[#-1][[-1, 1]]>FactorInteger[#+1][[-1, 1]], True]&] (* James C. McMahon, Jan 15 2024 *)
CROSSREFS
Cf. A023503 (greatest prime divisor of n-th prime - 1), A023509 (greatest prime divisor of n-th prime + 1), A103666, A070087.
Sequence in context: A284052 A211433 A039511 * A033207 A095084 A182569
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Feb 19 2005
STATUS
approved