

A024675


Average of two consecutive odd primes.


65



4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, 102, 105, 108, 111, 120, 129, 134, 138, 144, 150, 154, 160, 165, 170, 176, 180, 186, 192, 195, 198, 205, 217, 225, 228, 231, 236, 240, 246, 254, 260, 266, 270, 274, 279, 282, 288, 300
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OFFSET

1,1


COMMENTS

Sometimes called interprimes.
Where local maxima of A072681 occur: A072681(a(n))=A074927(n+1). [From Reinhard Zumkeller, Mar 04 2009]
Never prime, for that would contradict the definition.  Jon Perry, Dec 05 2012
A subset of A145025, obtained from that sequence by omitting the primes (which are barycenter of their neighboring primes).  M. F. Hasler, Jun 01 2013


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Interprime


FORMULA

a(n) = (prime(n+1)+prime(n+2))/2 = A001043(n+1)/2.  Omar E. Pol, Feb 02 2012
Conjecture: a(n) = ceiling(sqrt(prime(n+1)*prime(n+2))).  Thomas Ordowski, Mar 22 2013
A024675 = A145025 \ A006562 (= A145025 \ A000040).  M. F. Hasler, Jun 01 2013


MAPLE

seq( ( (ithprime(x)+ithprime(x+1))/2 ), x=2..40);


MATHEMATICA

Plus @@@ Partition[Table[Prime[n], {n, 2, 100}], 2, 1]/2
ListConvolve[{1, 1}/2, Prime /@ Range[2, 70]] (* JeanFrançois Alcover, Jun 25 2013 *)


PROG

(PARI) for(X=2, 50, print((prime(X)+prime(X+1))/2))  Hauke Worpel (thebigh(AT)outgun.com), May 08 2008
(PARI) first(n)=my(v=primes(n+2)); vector(n, i, v[i+1]+v[i+2])/2 \\ Charles R Greathouse IV, Jun 25 2013


CROSSREFS

Cf. A072568, A072569. Bisections give A058296, A079424.
Sequence in context: A171845 A157124 A162735 * A163656 A100915 A144922
Adjacent sequences: A024672 A024673 A024674 * A024676 A024677 A024678


KEYWORD

nonn,nice,easy


AUTHOR

Clark Kimberling


STATUS

approved



