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A075893 Average of three successive primes squared, (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3. 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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=3..41.

FORMULA

(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 *)

CROSSREFS

Cf. A133529, A084951, A133940.

Sequence in context: A094447 A020224 A063519 * A064901 A039482 A247676

Adjacent sequences:  A075890 A075891 A075892 * A075894 A075895 A075896

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

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Last modified May 30 06:51 EDT 2017. Contains 287302 sequences.