A075893 Average of three successive primes squared, (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3.

65, 113, 193, 273, 393, 577, 777, 1057, 1337, 1633, 1913, 2289, 2833, 3337, 3897, 4417, 4953, 5537, 6153, 7017, 8073, 9177, 10073, 10753, 11313, 12033, 13593, 15353, 17353, 18417, 20097, 21441, 23217, 24673, 26369, 28129, 29953, 31577, 33761

Offset: 3

Author

Zak Seidov, Oct 17 2002

Keywords

• easy
• nonn

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

Examples

			a(3)=65 because (prime(3)^2+prime(4)^2+prime(5)^2)/3=(5^2+7^2+11^2)/3=65.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..5000

Crossrefs

Cf. A133529, A084951, A133940.

Programs

Magma

[(NthPrime(n)^2+NthPrime(n+1)^2+NthPrime(n+2)^2)/3: n in [3..50]]; // Vincenzo Librandi, Aug 21 2018

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 *)

Formula

a(n) = (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3.

Extensions

Edited by N. J. A. Sloane, Jun 30 2008 at the suggestion of R. J. Mathar