A052288 First differences of the average of two consecutive primes (A024675).

2, 3, 3, 3, 3, 3, 5, 4, 4, 5, 3, 3, 5, 6, 4, 4, 5, 3, 4, 5, 5, 7, 6, 3, 3, 3, 3, 9, 9, 5, 4, 6, 6, 4, 6, 5, 5, 6, 4, 6, 6, 3, 3, 7, 12, 8, 3, 3, 5, 4, 6, 8, 6, 6, 4, 4, 5, 3, 6, 12, 9, 3, 3, 9, 10, 8, 6, 3, 5, 7, 7, 6, 5, 5, 7, 6, 6, 9, 6, 6, 6, 4, 5, 5, 7, 6, 3, 3, 8, 10, 6, 6, 6, 5, 9, 7, 10, 12, 8, 8, 6

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = (prime(n+3) - prime(n+1))/2.

a(n) = A115061(n+2) = A162345(n+2). - Nathaniel Johnston, Jun 25 2011

Example

a(30) = ((113 + 127)/2) - ((127 + 131)/2) = (131 - 113)/2 = 9;
a(31) = ((127 + 131)/2) - ((137 + 131)/2) = (137 - 127)/2 = 5.

Mathematica

Differences@ ListConvolve[{1, 1}/2, Prime@ Range[2, 120]] (* Michael De Vlieger, Dec 17 2016, after Jean-François Alcover at A024675 *)
Differences[Mean/@Partition[Prime[Range[2, 110]], 2, 1]] (* Harvey P. Dale, Sep 10 2024 *)

Crossrefs

Sequence in context: A277267 A246262 A275974 * A374942 A280455 A284725

Adjacent sequences: A052285 A052286 A052287 * A052289 A052290 A052291

Keyword

nonn,easy,changed

Author

Labos Elemer, Feb 08 2000

Status

approved