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

1,1

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.

Formula

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

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 *)

Prog

(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

Crossrefs

A bisection of A024675. Cf. A079424.

Sequence in context: A042960 A266596 A045975 * A347473 A025217 A119759

Adjacent sequences: A058293 A058294 A058295 * A058297 A058298 A058299

Keyword

easy,nonn

Author

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

Status

approved