cp's OEIS Frontend

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

%I A103667 #24 Jan 20 2024 18:20:52
%S A103667 7,11,23,29,31,47,53,59,71,79,83,89,103,107,127,131,139,149,167,173,
%T A103667 179,191,199,223,227,233,239,263,269,293,307,311,317,347,349,359,367,
%U A103667 373,383,389,419,431,439,449,461,467,479,499,503,509,557,563,569,571,587
%N A103667 Primes p such that the largest prime divisor of p-1 is greater than the largest prime divisor of p+1.
%C A103667 Primes of the form 2*A070087(n)+1 for some n. - _Charles R Greathouse IV_, Dec 22 2022
%C A103667 Conjecture: this sequence is of positive relative density in the primes, perhaps even 1/2. - _Charles R Greathouse IV_, Dec 22 2022
%H A103667 Karl Hovekamp, <a href="/A103667/b103667.txt">Table of n, a(n) for n = 1..39328</a>
%e A103667 a(1)=7 because the largest prime divisor of 6 is greater than the largest prime divisor of 8.
%p A103667 filter:= p -> isprime(p) and max(numtheory:-factorset(p-1)) > max(numtheory:-factorset(p+1)):
%p A103667 select(filter, [seq(i,i=3..1000,2)]); # _Robert Israel_, Jan 15 2024
%t A103667 Select[Prime@Range[2, 107], If[FactorInteger[#-1][[-1, 1]]>FactorInteger[#+1][[-1, 1]], True]&] (* _James C. McMahon_, Jan 15 2024 *)
%Y A103667 Cf. A023503 (greatest prime divisor of n-th prime - 1), A023509 (greatest prime divisor of n-th prime + 1), A103666, A070087.
%K A103667 nonn
%O A103667 1,1
%A A103667 _Hugo Pfoertner_, Feb 19 2005