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A024677 Smallest prime divisor of n-th 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 (list; graph; refs; listen; history; text; internal format)
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: A295784 A275803 A060131 * A276856 A174296 A163178

Adjacent sequences:  A024674 A024675 A024676 * A024678 A024679 A024680

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)