A103667 Primes p such that the largest prime divisor of p-1 is greater than the largest prime divisor of p+1.

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

Author

Hugo Pfoertner, Feb 19 2005

Keywords

• nonn

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

Examples

			a(1)=7 because the largest prime divisor of 6 is greater than the largest prime divisor of 8.
		

Links

• Karl Hovekamp, Table of n, a(n) for n = 1..39328

Crossrefs

Cf. A023503 (greatest prime divisor of n-th prime - 1), A023509 (greatest prime divisor of n-th prime + 1), A103666, A070087.

Programs

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 *)