A024677 - OEIS

%I #13 Nov 03 2019 19:48:30

%S 2,2,3,2,3,2,3,2,2,2,3,2,3,2,2,2,2,3,2,2,3,2,3,3,2,3,2,3,2,3,2,2,2,2,

%T 2,2,3,2,2,2,2,2,3,2,5,7,3,2,3,2,2,2,2,2,2,2,2,3,2,2,2,3,2,3,2,2,2,2,

%U 3,2,3,2,2,3,2,3,3,3,2,2,2,2,2,3,2,3,3,2,3,11,3,3,3,3,2,5,2,2,2

%N Smallest prime divisor of n-th terms of sequence A024675 (averages of two consecutive odd primes).

%C From _Robert Israel_, Nov 03 2019: (Start)

%C If prime(n+1) and prime(n+2) are twin primes, then a(n)=2.

%C If prime(n+1)>3 is in A023200, then a(n)=3.

%C Dickson's conjecture implies that for any prime p>3, there are infinitely many primes q>=p such that pq-6 and pq+6 are consecutive primes, so that a(pi(pq)-1) = p.  Thus each prime should occur infinitely many times in the sequence. (End)

%H Robert Israel, <a href="/A024677/b024677.txt">Table of n, a(n) for n = 1..10000</a>

%p P:= select(isprime,[seq(i,i=3..104759,2)]):

%p Q:= (P[2..-1]+P[1..-2])/2:

%p map(min @ numtheory:-factorset, Q); # _Robert Israel_, Nov 03 2019

%t Table[First@First@FactorInteger[(Prime[n+1]+Prime[n])/2],{n,2,150}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 25 2012 *)

%Y Cf. A023200

%K nonn

%O 1,1

%A _Clark Kimberling_