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

1,1

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

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 *)

Crossrefs

Cf. A023200

Sequence in context: A275803 A060131 A343391 * A276856 A174296 A163178

Adjacent sequences: A024674 A024675 A024676 * A024678 A024679 A024680

Keyword

nonn

Author

Clark Kimberling

Status

approved