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

Author

Labos Elemer, Feb 08 2000

Keywords

• nonn
• easy

Examples

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

Links

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

Programs

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 *)

Formula

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

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