This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A024677 #13 Nov 03 2019 19:48:30
%S A024677 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 A024677 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 A024677 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 A024677 Smallest prime divisor of n-th terms of sequence A024675 (averages of two consecutive odd primes).
%C A024677 From _Robert Israel_, Nov 03 2019: (Start)
%C A024677 If prime(n+1) and prime(n+2) are twin primes, then a(n)=2.
%C A024677 If prime(n+1)>3 is in A023200, then a(n)=3.
%C A024677 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 A024677 Robert Israel, <a href="/A024677/b024677.txt">Table of n, a(n) for n = 1..10000</a>
%p A024677 P:= select(isprime,[seq(i,i=3..104759,2)]):
%p A024677 Q:= (P[2..-1]+P[1..-2])/2:
%p A024677 map(min @ numtheory:-factorset, Q); # _Robert Israel_, Nov 03 2019
%t A024677 Table[First@First@FactorInteger[(Prime[n+1]+Prime[n])/2],{n,2,150}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 25 2012 *)
%Y A024677 Cf. A023200
%K A024677 nonn
%O A024677 1,1
%A A024677 _Clark Kimberling_