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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 (list; graph; refs; listen; history; text; internal format)
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]] (* Jean-Fran├žois 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

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Last modified December 22 00:41 EST 2014. Contains 252326 sequences.