OFFSET
3,1
COMMENTS
Unlike the average of three successive primes, the average of three successive primes (greater than 3) squared is always integral.
A133529(n)/3, n >= 3. - Artur Jasinski, Sep 30 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 3..5000
FORMULA
a(n) = (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3.
EXAMPLE
a(3)=65 because (prime(3)^2+prime(4)^2+prime(5)^2)/3=(5^2+7^2+11^2)/3=65.
MATHEMATICA
b = {}; a = 2; Do[k = (Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a)/3; AppendTo[b, k], {n, 3, 50}]; b (* Artur Jasinski, Sep 30 2007 *)
Mean[#]&/@Partition[Prime[Range[3, 50]]^2, 3, 1] (* Harvey P. Dale, Jun 09 2013 *)
PROG
(Magma) [(NthPrime(n)^2+NthPrime(n+1)^2+NthPrime(n+2)^2)/3: n in [3..50]]; // Vincenzo Librandi, Aug 21 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zak Seidov, Oct 17 2002
EXTENSIONS
Edited by N. J. A. Sloane, Jun 30 2008 at the suggestion of R. J. Mathar
STATUS
approved