

A024677


Smallest prime divisor of nth terms of sequence A024675 (averages of two consecutive odd primes).


1



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
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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 pq6 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: A295784 A275803 A060131 * A276856 A174296 A163178
Adjacent sequences: A024674 A024675 A024676 * A024678 A024679 A024680


KEYWORD

nonn


AUTHOR

Clark Kimberling


STATUS

approved



