A058296 Average of consecutive primes.

2, 4, 9, 15, 21, 30, 39, 45, 56, 64, 72, 81, 93, 102, 108, 120, 134, 144, 154, 165, 176, 186, 195, 205, 225, 231, 240, 254, 266, 274, 282, 300, 312, 324, 342, 351, 363, 376, 386, 399, 414, 426, 436, 446, 459, 465, 483, 495, 506, 522, 544, 560, 570, 582, 596

Offset: 1

Author

Donald Mills (dmills(AT)math.siu.edu), Feb 16 2003

Keywords

• easy
• nonn

Comments

2 together with average of odd primes taken two at a time without overlaps, i.e., 2 together with average of (3,5), (7,11), (13,17), etc. - Harvey P. Dale, Apr 09 2018

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Donald Mills, Some Interesting Sequences.

Crossrefs

A bisection of A024675.

Cf. A000040, A079424.

Programs

Maple

with(linalg): v := linalg[vector](100): v[1] := 2: for j from 2 to 100 do v[j] := (ithprime(2*j-2)+ithprime(2*j-1))/2: od: print(v);

Mathematica

Join[{2},Mean/@Partition[Prime[Range[2,121]],2]] (* Harvey P. Dale, Apr 09 2018 *)

PARI

{ write("b058296.txt", 1, " ", 2); p2=2; for (n=2, 20000, p1=nextprime(p2+1); p2=nextprime(p1+1); a=(p1+p2)/2; write("b058296.txt", n, " ", a); ); } \\ Harry J. Smith, May 30 2009

Formula

a(1)=2, a(n) = (prime(2n-2) + prime(2n-1))/2 for n>1, where prime(i) is the i-th prime.