A024677 Smallest prime divisor of n-th terms of sequence A024675 (averages of two consecutive odd primes).

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, 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, 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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

From Robert Israel, Nov 03 2019: (Start)

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

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

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)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023200

Programs

Maple

P:= select(isprime,[seq(i,i=3..104759,2)]):
Q:= (P[2..-1]+P[1..-2])/2:
map(min @ numtheory:-factorset, Q); # Robert Israel, Nov 03 2019

Mathematica

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