A103667 - OEIS

%I #24 Jan 20 2024 18:20:52

%S 7,11,23,29,31,47,53,59,71,79,83,89,103,107,127,131,139,149,167,173,

%T 179,191,199,223,227,233,239,263,269,293,307,311,317,347,349,359,367,

%U 373,383,389,419,431,439,449,461,467,479,499,503,509,557,563,569,571,587

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

%C Primes of the form 2*A070087(n)+1 for some n. - _Charles R Greathouse IV_, Dec 22 2022

%C Conjecture: this sequence is of positive relative density in the primes, perhaps even 1/2. - _Charles R Greathouse IV_, Dec 22 2022

%H Karl Hovekamp, <a href="/A103667/b103667.txt">Table of n, a(n) for n = 1..39328</a>

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

%p filter:= p -> isprime(p) and max(numtheory:-factorset(p-1)) > max(numtheory:-factorset(p+1)):

%p select(filter, [seq(i,i=3..1000,2)]); # _Robert Israel_, Jan 15 2024

%t Select[Prime@Range[2, 107], If[FactorInteger[#-1][[-1, 1]]>FactorInteger[#+1][[-1, 1]], True]&] (* _James C. McMahon_, Jan 15 2024 *)

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

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Feb 19 2005