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A052288
First differences of the average of two consecutive primes (A024675).
9
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
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
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Feb 08 2000
STATUS
approved