A052288 - OEIS

%I #14 Sep 10 2024 17:45:56

%S 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,

%T 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,

%U 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

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

%H Michael De Vlieger, <a href="/A052288/b052288.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A115061(n+2) = A162345(n+2). - _Nathaniel Johnston_, Jun 25 2011

%e a(30) = ((113 + 127)/2) - ((127 + 131)/2) = (131 - 113)/2 = 9;

%e a(31) = ((127 + 131)/2) - ((137 + 131)/2) = (137 - 127)/2 = 5.

%t Differences@ ListConvolve[{1, 1}/2, Prime@ Range[2, 120]] (* _Michael De Vlieger_, Dec 17 2016, after _Jean-François Alcover_ at A024675 *)

%t Differences[Mean/@Partition[Prime[Range[2,110]],2,1]] (* _Harvey P. Dale_, Sep 10 2024 *)

%K nonn,easy

%O 1,1

%A _Labos Elemer_, Feb 08 2000